Question

show that
(4/3m - 3/4n)²+2nm=16/9m²+9/16n²



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Answer 1

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.

(ii) a² - b² = (a + b) (a - b)

L.H.S. = (4pq + 3q)² - (4pq - 3q)²

= (4pq + 3q + 4pq - 3q) (4pq + 3q - 4pq + 3q)

= 8pq * 6q

= 48pq² = R.H.S.

Hence, proved.