Question

Evaluate using suitable identities.
If 2x + 3y = 16 and xy = 10 , find the value of 4x^2 + 9y^2​

Answer 1

Step-by-step explanation:

Given,

2x + 3y = 16

xy = 10

squaring on both sides

(2x + 3y )² = 16² (Using identity (a + b )² = a² + b² + 2ab )

= 4x² + 9y ² + 2 (2x)(3y) = 256

= 4x² + 9y² + 12xy = 256

xy = 10

therefore , 12xy = 12 × 10 = 120

= 4x² + 9y² + 120 = 256

4x² + 9y² = 256 - 120

4x² + 9y² = 136

Answer 2

GIVEN :–

• 2x + 3y = 16

• xy = 10

TO FIND :–

• 4x² + 9y² = ?

SOLUTION :–

=> 2x + 3y = 16

• Square on both sides –

=> (2x + 3y)² = (16)²

▪︎ Using identity –

☆ (a + b)² = a² + b² + 2ab

• So that –

=> (2x)² + (3y)² + 2(2x)(3y) = 256

=> 4x² + 9y² + 2(6xy) = 256

=> 4x² + 9y² + 12(xy) = 256

=> 4x² + 9y² + 12(10) = 256

=> 4x² + 9y² + 120 = 256

=> 4x² + 9y² = 256 - 120

=> 4x² + 9y² = 136

▪︎ Hence , The value of 4x² + 9y² = 136.