Question

if 3x +2y=12 and xy =6 find the value of 9x²+4.

Answer 1

Step-by-step explanation:

9x²+4=(3x + 2y )² -3xy

=(12)²-3.6

=144-18

=136

:. 9x²+4=136 ans

Answer 2

Question :

If 3x + 2y = 12 and xy = 6 , find the value of 9x² + 4y² .

Answer :

9x² + 4y² = 72

Note :

• (A + B)² = A² + B² + 2AB

• (A - B)² = A² + B² - 2AB

• (A + B)(A - B) = A² - B²

• A³ + B³ = (A + B)(A² + B² - AB)

• A³ - B³ = (A - B)(A² + B² + AB)

• (A + B)³ = A³ + B³ + 3AB(A + B)

• (A - B)³ = A³ - B³ - 3AB(A - B)

Solution :

• Given : 3x + 2y = 12 , xy = 6
• To find : 9x² + 4y² = ?

We have ;

3x + 2y = 12

Now ,

Squaring both the sides , we get ;

=> (3x + 2y)² = 12²

{ using identity (A + B)² = A² + B² + 2AB }

=> (3x)² + (2y)² + 2•3x•2y = 144

=> 9x² + 4y² + 12xy = 144

=> 9x² + 4y² + 12•6 = 144

=> 9x² + 4y² + 72 = 144

=> 9x² + 4y² = 144 - 72

=> 9x² + 4y² = 72

Hence ,

9x² + 4y² = 72