Find the value of 9×2 + 16y2.

If 3x – 4y = 16 and xy = 4, find the value of 9x² + 16y².

Answer :

We know that

(3x – 4y)² = 9x² + 16y² – 24xy

It can be written as

9x² + 16y² = (3x – 4y)² + 24xy

It is given that

3x – 4y = 16 and xy = 4

Substituting the values

9x² + 16y² = 16² + 24 × 4

By further calculation

= 256 + 96

= 352

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