Question

If (A +B)square2 = 100 and A:B =2:3 then AB?​

Answer 1

Answer:

This your correct answer....see this attachment

Answer 2

Correct Question :

• If (A +B)² = 100 and A : B = 2 : 3 then AB ?

Given :

• (A + B)² = 100
• A : B = 2 : 3

To find :

• Find AB ?

$\large\star$ As we know that,

$\large\dag$ Formula Used :

• $\boxed{\bf{(a + b)^2\:=\:a^2\:+\:b^2\:+\:2ab}}$$\large\dag$

Solution :

:$\implies{\sf{A \:= \:2x\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;B\:=\:3x}}$

$:\implies{\sf{100\:=\:(2x)^2\:+\:(2x)(3x)\:+\:(3x)^2}}$

$:\implies{\sf{100\:=\:4x^2\:+\:12x^2\:+\:9x^2}}$

$:\implies{\sf{100\:=\:x^{2}(4\:+\:12\;+\:9)}}$

$:\implies{\sf{100\:=\:x^{2}(25)}}$

$:\implies{\sf{x^2\:=\:\cancel{\dfrac{100^{4}}{25}}}}$

$:\implies{\sf{x^2\:=\:4}}$

$:\implies{\sf{x\:=\:4\:-\:2}}$

$:\implies{\underline{\boxed{\frak{\pink{x\:=\:2}}}}}$★

Hence,

• ${\underline{\sf{The\: value\;of\:\bf{x}\:\sf{is}\:\bf{2}.}}}$