common.or
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What should be the values of a and b for which 64x2−9ax2+108x-b will be a perfect cube?
we know, x-y3=x3-3x2y+3xy2-y3Now, 64x3-9ax2+108x-b=4x3-3×4x2×3+3×4x×32-33=4x-33In here, in the 2nd term 3×4x2×3=3×42×x2×3So,in here 42=16=aIn the 3rd term= 3×4x×32 [3xy2]And in 4th terrm= 33 = bSo, b=33=27 ans. a=16 & b=27
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