bhai kaisa?? bhai we can also represent other numbers also na?.. like 8^2 - 6^2 = 28(not prime)
dude , whats the answer..? m sure about about mutiples of 4 , and odd nos. evn 28 is mutiple of 4.. as far as uniquely is concerned - evry triplet is different , so all triples till 100 will be unique only , so no. of triplets = 75 but exclude 1 so 74?
@CSK23Shld be 74 i thnk..Here, x^2 - y^2 = k..,or, (x+y)(x-y) = k..Here, a General Observation can be made: 1, 2, 6, 10......98 cannot be expressed as a difference of 2 perfect squares..Thus, Required Number = 100 - (1, 2, 6, 10.., 98)=> 100 - 26 = 74..
i thought the same, however a slight change... we need to pay attention to the word uniquely...
now 21 = 7*3 and 21*1 so it can be expressed in two ways...
the numbers have to be prime....
or exceptions are 4*prime like 36
so when we write 2*18 we can express it as required
take a smaller case...product of factors of 25 which are divisible by 5...25 = 5^25(5) = 25^2(1) = 1hence, total power of 5 = 3...so here when 5^2*5*1 = 5^3hope it is clear that it does not get twice...
what i failed to take into account was that the cases are not mutually exclusive. one includes the other. thanx
Here, The triangle BOC is similar to DOA and not AOD, In similarity of triangles its important to take correct sequence of letters as it helps to right correct ratios.
Now, Here In BOC and DOA
angle BOC = Angle DOA ( opposite angles)
Also, angle B = angle D
and angle C = angle A ( Alternate angles)
BOC similar to DOA
So,
BO / DO = OC / OA
I hope you guys got it. Let me know if there,s a confusion.
Here, The triangle BOC is similar to DOA and not AOD, In similarity of triangles its important to take correct sequence of letters as it helps to right correct ratios.Now, Here In BOC and DOAangle BOC = Angle DOA ( opposite angles)Also, angle B = angle Dand angle C = angle A ( Alternate angles)BOC similar to DOASo,BO / DO = OC / OAI hope you guys got it. Let me know if there,s a confusion.
a^2-b^2= (a+b)(a-b); and a , b are integers.. ; to be able to equate and find a, b - both (a+b) (a-b) should be either even or both odd ; even*even= multiple of 4 ; odd*odd= odd^2 or odd1*odd2(in case odd are different) but cases like 9 , 40 , 41 n many others do exist.. ; so we cant include just prime no.s but rather including all mutiples of 4 and odd no.s be inclusive :)
every odd number is a part of a pythagorian triplet except 1, and hence it can be expressed as a difference of 2 squares.3,4,5 ---- 3^2 = 5^2 - 4^25,12,13 ---- 5^2 = 13^2 - 12^2..so all odd nos less than 100 can be expressed as a difference of 2 squares = 49i dont understand "uniquely"
let me try and take what uniquely here means....
this question basically asks us to find out the number of numbers which can be expressed as the difference of squares of two number in exactly one way (uniquely)...
for example
x^2 - y^2 = 28
x and y have only 1 value (+ve integer) viz x=8 and y=6
8^2 - 6^2 = 28
there is no other way of writing 28 in x^2-y^2 form except for this...
whereas take any random non-prime odd number, say 33
x^-y^2 = 33 can be expressed as 17^2-16^2 or 7^2-4^2 -> which are 2 ways and hence not unique...
If the two vertices of an isosceles triangle ABC are B(5,7) and c(-4,3), then the vertex A can be?a. (1/2,5)b. (11/6,2)c. (3,4)d. None of these.Please mention the approach as well...
If the two vertices of an isosceles triangle ABC are B(5,7) and c(-4,3), then the vertex A can be?a. (1/2,5)b. (11/6,2)c. (3,4)d. None of these.Please mention the approach as well...
@Logrhythm the answer is b could you please mention the appraoch that you used for solving this one. I assume that you used AB=AC.......But my question is how does one figure out for sure that the two equal sides are AB and AC and not BC ,AC and or AB,BC?
If the two vertices of an isosceles triangle ABC are B(5,7) and c(-4,3), then the vertex A can be?a. (1/2,5)b. (11/6,2)c. (3,4)d. None of these.Please mention the approach as well...
haan correct, answer wld be b..@pyashraj bhai in option A...the condition a+b > c for a trngl is not getting fullfilled....badia question...kya trick daali..
Ohh....Sahi hai yaar...Didn't thought with that angle.
