Question

if 3 X + 2 Y is equal to 12 and X Y is equal to 6 find the value of 9 X square + 4 y square​

Answer 1

Given :-

• 3x + 2y = 12

$•xy = 6$

To Find :-

• Value of 9x² + 4y²

Solution :-

Given that,

3x + 2y = 12 and xy = 6

Formula to be used :-

a² + b² = (a+b)² -2ab

As per question, we need to find the value of 9x² + 4y².

Hence,

⟼ 9x² + 4y²

= (3x + 2y)² - 2 × 3x ×2y

= (3x + 2y)² - 12xy

Now put the given values

= ( 12)² - 12 × 6

= 72

Hence, the value of 9x² + 4y² is = 72

Extra Information :-

•Some identities :-

1. (a + b)² = a² + 2ab + b²

2. (a – b)² = a² – 2ab + b²

3. (x + a)(x + b) = x² + (a + b)x + ab

4. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

5. a³ – b³ = (a – b)(a² + ab + b²)

6. (a + b)³ = a³ + 3a²b + 3ab² + b³

7. (a – b)³ = a³ – 3a²b + 3ab² – b³

8.a³ + b³ = (a + b)(a² – ab + b²)