Showthat(3⁄4m–3⁄4n)2 +2mn=16/9 m2+9/16n
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Answer:
Use of algebraic identities:
(i) (a - b)² = a² - 2ab + b²
L.H.S. = (4/3 m - 3/4 n)² + 2mn
= (4/3 m)² - 2 * 4/3 m * 3/4 n + (3/4 n)² + 2mn
= 16/9 m² - 2mn + 9/16 n² + 2mn
= 16/9 m² + 9/16 n² = R.H.S.
Hence, proved.
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