If 2x - 3y - 8 and xy - 2- find the value of 4x2 - 9y2-

2x + 3y = 8 and xy = 2 Now, (2x + 3y)2 = (2x)2 + (3y)2 + 2 x 2x x 3y ⇒ (8)^2=4x^2+9y^2+12xy ⇒ 64= 4x^2+9y^2+24 ⇒ 64=4x^2+9y^2+24 ⇒ 4x^2+9y^2=64 24=40 ∴ 4x^ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Multiplication of Two Binomials

If 2x + 3y = ...

Question

If 2x + 3y = 8 and xy = 2, find the value of 4x² + 9y^2.

Open in App

Solution

2x + 3y = 8 and xy = 2
Now, (2x + 3y)² = (2x)² + (3y)² + 2 x 2x x 3y
$\Rightarrow (8)^{2} = 4 x^{2} + 9 y^{2} + 12 x y \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 24 \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 24 \Rightarrow 4 x^{2} + 9 y^{2} = 64 - 24 = 40 ∴ 4 x^{2} + 9 y^{2} = 40$

Suggest Corrections

Similar questions

Q. If

(2 x - 3 y) = 10

and

x y = 8

, find the value of

4 x^{2} + 9 y^{2}

Q. If

2 x \div 3 y = 8

and

x y = 4

then find the value of

4 x^{2} + 9 y^{2}

Q. If

4 x^{2} + 9 y^{2} = 40, x y = 2

, find

2 x + 3 y

Q. Find the product :
(i) (2x + 3y) (2x - 3y)

(4 x^{2} + 9 y^{2}

)

Find the product of $(2 x - 3 y)$ and $(4 x^{2} + 9 y^{2} + 6 x y)$ .

Join BYJU'S Learning Program

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

2x + 3y = 8 and xy = 2 Now, (2x + 3y)2 = (2x)2 + (3y)2 + 2 x 2x x 3y ⇒ (8)2=4x2+9y2+12xy⇒ 64=4x2+9y2+24⇒ 64=4x2+9y2+24⇒ 4x2+9y2=64−24=40∴ 4x2+9y2=40

If 2x + 3y = 8 and xy = 2, find the value of 4x² + 9y^2.

2x + 3y = 8 and xy = 2
Now, (2x + 3y)² = (2x)² + (3y)² + 2 x 2x x 3y
$\Rightarrow (8)^{2} = 4 x^{2} + 9 y^{2} + 12 x y \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 24 \Rightarrow 64 = 4 x^{2} + 9 y^{2} + 24 \Rightarrow 4 x^{2} + 9 y^{2} = 64 - 24 = 40 ∴ 4 x^{2} + 9 y^{2} = 40$