@karl said:Sorry for the typo, question is Maximize (13-x)^7 *(X+7)^3. sorry lazy habits
2^10*3^3*7^7 :lookround:
@karl said:Sorry for the typo, question is Maximize (13-x)^7 *(X+7)^3. sorry lazy habits
in that case the underlying logic still remains the same except that you need a bit of mathematical jugglery.
(13-x)^7 * (x+7)^3 can be written as
(7^7*3^3) * [(13-x)/7]^7 * [(x+7)/3]^3
now (13-x) + (x+7) =20 can be written as
7*(13-x)/7 + 3*(x+7)/3 =20
we know AM >=GM
=>20/(7+3) >= [{(13-x)/7}^7 * {(x+7)/3}^3]^(1/10)
=>2^10 >= [{(13-x)/7}^7 * {(x+7)/3}^3]
and equality occurs when each term = AM
=>at (13-x)/7 = 2 maxima would occur
=> at x=-1 [{(13-x)/7}^7 * {(x+7)/3}^3] will be maximum and its value = 2^10
Hence max value of the expression = (7^7)*(3^3)*(2^10).
ATDH.
@anytomdickandhary said:in that case the underlying logic still remains the same except that you need a bit of mathematical jugglery.(13-x)^7 * (x+7)^3 can be written as(7^7*3^3) * [(13-x)/7]^7 * [(x+7)/3]^3now (13-x) + (x+7) =20 can be written as7*(13-x)/7 + 3*(x+7)/3 =20we know AM >=GM=>20/(7+3) >= [{(13-x)/7}^7 * {(x+7)/3}^3]^(1/7)=>128 >= [{(13-x)/7}^7 * {(x+7)/3}^3]and equality occurs when each term = AM=>at (13-x)/7 = 2 maxima would occur=> at x=-1 [{(13-x)/7}^7 * {(x+7)/3}^3] will be maximum and its value = 128Hence max value of the expression = (7^7)*(3^3)*(128).ATDH.
Understood, your method, but you committed a silly mistake at the end of it. The question was Maximum value of " (13-x)^7*(x+7)^3", in the last step you divided that by 7^7 and 3^3.
Yeah, familiar with these questions, AIMCAT used to ask these questions like Hot cakes, but not any more.
@karl said:Understood, your method, but you committed a silly mistake at the end of it. The question was Maximum value of " (13-x)^7*(x+7)^3", in the last step you divided that by 7^7 and 3^3.Yeah, familiar with these questions, AIMCAT used to ask these questions like Hot cakes, but not any more.
Aap bade date khiladi lag rahe ho 😁 "used to... not anymore"
@ashishpai2001 said:Aap bade date khiladi lag rahe ho "used to... not anymore"
the correct phrase is "but not any more", @ankita14 ko pata hoga, nahi yaar bas puraani baate yaad aa jaati hain, abhi to lagi padi hui hai :(
@Brooklyn said:@anytomdickandhary : i used differentiantion
that is equally good....... however I would use my method because it would be faster for me.
using this method I can literally do a bit of mental calculations and mark the answer right away. If you get the key steps of this process it doesn't take more than 45 secs to solve problems of this type.
However while applying this method following are the tricky points which can lead to incorrect answers.
1. Make sure that value of the terms is +ve.
2. Value of x at which we find max or min must lie within the range (if given!). In the problem under discussion range is defined as -7
ATDH.
Find the number of ways to paint a cube with only two colors? red and blue
@karl said:the correct phrase is "but not any more", @ankita14 ko pata hoga, nahi yaar bas puraani baate yaad aa jaati hain, abhi to lagi padi hui hai
It's the same everywhere.
@karl said:Understood, your method, but you committed a silly mistake at the end of it. The question was Maximum value of " (13-x)^7*(x+7)^3", in the last step you divided that by 7^7 and 3^3.Yeah, familiar with these questions, AIMCAT used to ask these questions like Hot cakes, but not any more.
yeah I realised my calculation mistake. Thats a constant problem for me. Please refer to my signature.... below.
ATDH.
a,b and c are three positive natural numbers with HCF = 8.
a -b = b -c = 1 and LCM of a,b,c is a 4 digit number..find the max possible value of c..?
a -b = b -c = 1 and LCM of a,b,c is a 4 digit number..find the max possible value of c..?
@anytomdickandhary said:yeah I realised my calculation mistake. Thats a constant problem for me. Please refer to my signature.... below.ATDH.
Haha, same with me but mine is more embarrassing for sure,
@gyrodceite said:a,b and c are three positive natural numbers with HCF = 8.a -b = b -c = 1 and LCM of a,b,c is a 4 digit number..find the max possible value of c..?
:O
Consecutive natural numbers have HCF = 1 na?
@gyrodceite said:a,b and c are three positive natural numbers with HCF = 8.a -b = b -c = 1 and LCM of a,b,c is a 4 digit number..find the max possible value of c..?
question yehi hai, Let a,b,c be 8x,8y,8z as 8 is the HCF.
So, a-b = 8(x-y)=8(y-z)=1.... can you check question or point me my mistake.
@gyrodceite said:Find the number of ways to paint a cube with only two colors? red and blue
6c1 *2c1 + 6c2*c1 so on 2^6 * 2c1 = 2^7 ??