Question

3a+4b = 16 & ab=4,find the value of 9a^2 +16b^2

Answer 1

Step-by-step explanation:

Given -

• 3a + 4b = 16
• ab = 4

To Find -

• Value of 9a² + 16b²

Now,

→ 3a + 4b = 16

Squaring both sides :-

→ (3a + 4b)² = (16)²

→ (3a)² + (4b)² + 2×(3a)×(4b) = 256

→ 9a² + 16b² + 24ab = 256

→ 9a² + 16b² + 24×(4) = 256

→ 9a² + 16b² = 256 - 96

→ 9a² + 16b² = 160

Hence,

The value of 9a² + 16b² is 160

Answer 2

Given:-

• 3a + 4b = 16
• ab = 4

To find:-

• 9a² + 16ab²

Solution:-

$\implies$ 3a + 4b = 16

✧ Squaring both sides:-

(3a + 4b)² = (16)²

(3a)² + 2 × 3a × 4b + (4a)² = 256

9a² + 24ab + 16b² = 256

✧ Putting the We given value of ab,

9a² + 25 × 4 + 16b² = 256

9a² + 96 + 16b² = 256

9a² + 16b² = 256 - 96

9a² + 16b² = 160

★ Hence, we have the value of 9a² + 16b²

$\implies$ 9a² + 16b² = 160

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