Question

If (x +1)(x + 2)(x+3)(x + 4) = 24 and (a + 4)(a + 6) = 24 then the relation between x and a is
(B) x² + 3x = a
(A) x2 + 2x=a
(C) x2 + 5x = a
(D) x +7x = a​

Answer 1

Given :   (x +1)(x + 2)(x+3)(x + 4) = 24 and (a + 4)(a + 6) = 24

To Find :  the relation between x and a  

(A) x² + 2x=a

(B) x² + 3x = a

(C) x² + 5x = a

(D) x² +7x = a​

Solution:

 (x +1)(x + 2)(x+3)(x + 4) = 24

=> (x + 1)(x + 4) (x + 2)(x + 3) = 24

=> (x² + 5x + 4)(x² + 5x + 6) = 24

Comparing with

(a + 4)(a +6) = 24

=> a = x² + 5x

Correct option is (C) x² + 5x = a

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Answer 2

Question :-

If (x +1)(x + 2)(x+3)(x + 4) = 24 and (a + 4)(a + 6) = 24 then the relation between x and a is

(B) x² + 3x = a

(A) x2 + 2x=a

(C) x2 + 5x = a

(D) x +7x = a

Answer :-

• (C) x² + 5x = a

Step by step explanation :-

In the question we have given that the two expressions and we have to find the relation between them.

Method of solving,

First we solve as possible as the given expression then we compare both.

$\: \: \: \: \:$⇒ (x + 1) (x + 2) (x + 3) (x + 4) = 24

$\: \: \: \: \:$⇒ (x + 1) (x + 4) (x + 2) (x + 3) = 24

$\: \: \: \: \:$⇒ x(x + 4) + 1(x + 4) (x + 2) (x + 3) = 24

$\: \: \: \: \:$⇒ (x² + 4x + x + 4) (x + 2) (x + 3) = 24

$\: \: \: \: \:$⇒ (x² + 5x + 4) x(x + 3) + 2 (x + 3) = 24

$\: \: \: \: \:$⇒ (x² + 5x + 4) x² + 3x + 2x + 6 = 24

$\: \: \: \: \:$⇒ (x² + 5x + 4) (x² + 5x + 6) = 24

Now,

$\: \: \: \: \:$⇒ (x² + 5x + 4) (x² + 5x + 6) = 24

$\: \: \: \: \:$⇒ (a + 4)(a + 6) = 24

Comparing both,

$\: \: \: \: \:$⇒ x² + 5x = a

Hence,

(C) x2 + 5x = a

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