Question

Find the value of 125p³ - 8q³ if 5p - 2q = 1 and pq = 2​

Answer 1

Step-by-step explanation:

$\huge\bf\orange{Given:-}$

5p-2q=1 & pq=2.

$\huge\bf\orange{To find out:-}$

$Value \: of \: 125p {}^{3} - 8q {}^{3}$

$\huge\bf\orange{Solution:-}$

$125p {}^{3} - 8q {}^{3} = (5p) {}^{3} - (2q) {}^{3} \\ = (5p - 2q) {}^{3} + 3 \times 5p \times 2q(5p - 2q) \\ = 1 {}^{3} + 30pq \times 1 \\ = 1 + 30 \times 2 \times 1 \\ = 1 + 60 \\ = 61$

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