i think oa is 74 -8 =64because all the odd terms and multiples of 4 can be expressed as difference of squares odd terms excluding 1 = 49 multiples of 4 = 2549+25 =74 - ( multiples of 12 coz they repeated )74-8 =66plz tell if iam right or wrong in appproach..
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong.. n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;
reason.. a^2 will need certain b^2 to form c^2.. if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..
for eg ; 3 , 4 ,5 5,12,13 7,24,25 8,15,17 9,40,41.. n so on... now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum.. that be unque..
[x] denotes the greatest integer value just below x{x} denotes the fraction value Sum of [x]^3 and {x}^2 = -7.91; Find x ?a.) -2.03b.) -1.97c.) -2.97d.) -1.7Please tell the approach !
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong..n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;reason.. a^2 will need certain b^2 to form c^2..if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..for eg ;3 , 4 ,5 5,12,137,24,258,15,179,40,41.. n so on...now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum..that be unque..
i am trying to say what about numbers 12 , 24 , 36......96 ..
no... not repeated coz odd no. doesn include odd mutiples of 4.. wrong..n such 74 be unique only ; since u can write a no.^2 as a differnc of 2 no.^2 only in 1 way ;reason.. a^2 will need certain b^2 to form c^2..if u add sum x^2 to a^2 it wont yield a perfect square ; these no. r unique..for eg ;3 , 4 ,5 5,12,137,24,258,15,179,40,41.. n so on...now we r luking for jus the 1st 2terms here, did a single one repeat?? no... 5^2= 3^2 + 4^2 , 5^2=13^2-12^2 , but in 1st case its not a differnc but a sum.. we r tokin of differnc here, not sum..that be unque..
[x] denotes the greatest integer value just below x{x} denotes the fraction value Sum of [x]^3 and {x}^2 = -7.91; Find x ?a.) -2.03b.) -1.97c.) -2.97d.) -1.7Please tell the approach !
[x]^3 has to be -ve (as we are getting a -ve sum...
{x}^2 is always +ve no matter what..
also [x]^3 > 7 (as a +ve number is getting added to it and still the sum remains > 7)
so option b and d are discarded...
now, (-2)^3 = -8
-8+{x}^2 = -7.91
{x}^2 = 0.09
{x} = +/- 0.3
hence x = -2.3
are the option correct?? 2.03 ki jagaah 2.3 hona chaie (in option a)