Question

Solve (x+1)(x+2)=(x+11)(x-2)​

Answer 1

Answer:

(x + 3) : (x + 11) = (x - 2) : (x + 1)

∴ (x + 3)(x +1) = (x – 2)(x + 11)

∴ x(x +1) + 3(x + 1) = x(x + 11) – 2(x + 11)

∴ x2 + x + 3x + 3 = x + x – 2x – 22

∴ x2 + 4x + 3 = x2 + 9x – 22

∴ 4x + 3 = 9x – 22

∴ 3 + 22 = 9x – 4x

∴ 25 = 5x

∴ x = 5

Answer 2

ANSWER:

To Solve:

• (x + 1) × (x + 2) = (x + 11) × (x - 2)

Solution:

We are given that,

$\implies (x+1)(x+2)=(x+11)(x-2)$

Opening brackets,

$\implies x^2+x+2x+2=x^2+11x-2x-22$

Cancelling x^2,

$\implies x^2\!\!\!\!/\:+3x+2=x^2\!\!\!\!/\:+9x-22$

$\implies 3x+2=9x-22$

Transposing 3x to RHS, and 22 to LHS,

$\implies 2+22=9x-3x$

$\implies 24=6x$

$\implies 6x=24$

Transposing 6 to RHS,

$\implies x=\dfrac{24\!\!\!\!\!/{\:\:4}}{6\!\!\!/_{\:1}}$

$\implies\bf x=4$

Hence, value of x = 4.

Verification:

We are given that,

$\implies (x+1)(x+2)=(x+11)(x-2)$

Substituting value of x as 4,

$\implies (4+1)(4+2)=(4+11)(4-2)$

$\implies 5\times6=15\times2$

$\implies 30=30$

As LHS = RHS,

HENCE VERIFIED!!