Question

If 2x + 3y = 11 and xy = 8, find the value of 4x2 +9y2.
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Answer 1

Answer:

25

Step-by-step explanation:

Given that,

2x + 3y = 11

And

xy = 8

To find the value of 4x^2 + 9y^2.

Simplifying further, we will get,

= (2x)^2 + (3y)^2

It's in the form of a^2 + b^2

We can write,

• a^2 + b^2 = (a+b)^2 -2ab

Therefore, we will get,

= (2x+3y)^2 - 2(2x)(3y)

= (2x+3y)^2 - 12xy

Substituting the values, we get,

= (11)^2 - 12(8)

= 121 - 96

= 25

Hence, the required value is 25.

Answer 2

ANSWER :–

$\\ \longrightarrow \large{ \boxed{ \bold{4 {x}^{2} + 9 {y}^{2} = 25 }}}$

EXPLANATION :–

GIVEN :–

• 2x + 3y = 11

• xy = 8

TO FIND :–

• 4x² + 9y² = ?

SOLUTION :–

• According to the first condition –

$\\ { \bold{2x + 3y = 11}}$

• Take Square on both side –

$\\ \implies{ \bold{(2x + 3y) {}^{2} = (11) {}^{2} }}$

• We know that –

$\\ \longrightarrow \: \large{ \boxed{ \bold{( a + b ) {}^{2} = {a}^{2} + {b}^{2} + 2ab}}}$

• So that –

$\\ \implies{ \bold{(2x ) {}^{2} + (3y) {}^{2} + 2(2x)(3y) = 121 }}$

$\\ \implies{ \bold{4 {x}^{2} + 9 {y}^{2} + 12xy = 121 }}$

$\\ \: \: \: { \bold{ \because \: \: xy = 8}}$

• So that –

$\\ \implies{ \bold{4 {x}^{2} + 9 {y}^{2} + 12 (8) = 121 }}$

$\\ \implies{ \bold{4 {x}^{2} + 9 {y}^{2} + 96 = 121 }}$

$\\ \implies{ \bold{4 {x}^{2} + 9 {y}^{2} = 121 - 96 }}$

$\\ \implies \large{ \boxed{ \bold{4 {x}^{2} + 9 {y}^{2} = 25 }}}$

$\\ \rule{220}{2}$