Question

Find 25x2 + 16y2, if 5x + 4y = 8 and xy = 1.

Answer 1

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If 5x−4y=7 and xy=8 , then find 125x

3

−64y

3

.

Medium

Solution

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Correct option is A)

5x−4y=7

Cubing both sides,

(5x−4y)

3

=7

3

Applying the formula,(a−b)

3

=a

3

−b

3

−3ab(a−b)

∴(5x)

3

−(4y)

3

−3×5x×4y×(5x−4y))=343

(5x)

3

−(4y)

3

−60×xy×(5x−4y)=343

Substituting, 5x−4y=7;xy=8

∴125x

3

−64y

3

−60×8×7=343

125x

3

−64y

3

=343+3360=3703