Question

The equation
24x2+25x−47
ax−2
=−8x−3−
53
ax−2
is true for all values of x≠
2
a
, where a is a constant.

What is the value of a?

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Answer 1

Explanation:

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answer

Given,

24x²+25x−47 = −8x−3− 53

ax−2 ax−2

⇒ 24x²+25x−47

ax−2

= (−8x−3)(ax−2)−53

ax−2

⇒24x²+25x−47=(−8x−3)(ax−2)−53

⇒24x²+25x−47=−8ax²+16x−3ax+6−53

⇒24x²+25x−47=−8ax²+16x−3ax−47

⇒24x²+25x=−8ax²+(16−3a)x

⇒24=−8a

⇒a=−3

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Answer 2

Answer:

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Explanation:

You seem to have missed something from the question! I think it should read ‘… is true for all values of x, except when …’

Let’s start by multiplying both sides of the equation by (ax−2) :

24x2+25x−47=(ax−2)(−8x−3)−53

Adding 53 to both sides of the equation: 24x2+25x+6=(ax−2)(−8x−3)

Multiply out the terms in parentheses: 24x2+25x+6=−8ax2+16x−3ax+6

Subtracting (16x+6) from both sides of the equation: 24x2+9x=−8ax2−3ax

Adding 8ax2+3ax to both sides of the equation: 24x2+8ax2+9x+3ax=0

Factorising: 8(3+a)x2+3(3+a)x=0

For this to be true for a general value of x , we require the coefficients of x2 and x to be zero ⇒a=−3

Of course, as clearly pointed out in the question, we can’t have ax=2⇒−3x≠2⇒x≠−23

Answer: a = -3