Question

if 3x+2y=12, xy=6 find 9x square + 4y square​

Answer 1

ANSWER:

• Value of the above expression is 72.

GIVEN:

• 3x+2y = 12
• xy = 6 ....(i)

TO FIND:

• 9x²+4y²

SOLUTION:

=> 3x+2y = 12

Squaring both sides we get;

=> (3x+2y)² = (12)²

=> (3x)²+(2y)²+2(3x)(2y) = 144

=> 9x²+4y²+12xy = 144

Putting xy = 6 from eq(i)

=> 9x²+4y²+12(6) = 144

=> 9x²+4y² = 144-72

=> 9x²+4y² = 72

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

72

Step-by-step explanation:

Given:

3x + 2y = 12

xy = 6

To find:

9x² + 4y²

How to get Answer ?

1. Square the both side
2. Recover the Algebra Formula
3. Substitute the given value

Solution:

3x + 2y = 12

[Squaring both side]

or, (3x + 2y)² = 12²

or, 9x² + 4y² + 2.3x.2y = 144

or, 9x² + 4y² + 12xy = 144

[Putting the value of xy]

or, 9x² + 4y² + 12.6 = 144

or, 9x² + 4y² + 72 = 144

or, 9x² + 4y² = 144 - 72

or, 9x² + 4y² = 72

Therefore, the required answer is 72.

Algebra Formula

${(x + y)}^{2}={x}^{2}+{y}^{2}+2xy\\ \\{(x - y)}^{2}={x}^{2}+{y}^{2}-2xy\\ \\{(x+y)}^{2}= (x - y) {}^{2}+4xy\\ \\{(x-y)}^{2}=(x+y){}^{2}-4xy\\ \\ (x + y)^{2}+(x-y)^{2}=2( {x}^{2}+{y}^{2} )\\ \\(x+y)^{2}- (x-y) {}^{2}=4xy$