What should be the values of a and b for which $64x2−9ax2+108x-b will be a perfect cube?$

Question

What should be the values of a and b for which <math xmlns="http://www.w3.org/1998/Math/MathML">64x2−9ax2+108x-b will be a perfect cube?

Satt Academy · Accepted Answer

we know, x-y3=x3-3x2y+3xy2-y3 Now, 64x3-9ax2+108x-b =4x3-3×4x2×3+3×4x×32-33 =4x-33 In here, in the 2nd term 3×4x2×3=3×42×x2×3 So,in here 42=16=a In the 3rd term= 3×4x×32 [3xy2] And in 4th terrm= 33 = b So, b=33=27 ans.a=16&b=27

What should be the values of a and b for which $64 x^{2} - 9 a x^{2} + 108 x - b$ will be a perfect cube?