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Question: The equation (x<sup>2</sup> + x + 1)<sup>2</sup> + 1 = (x<sup>2</sup> + x + 1) (x<sup>2</sup> –x – 5...

The equation (x2 + x + 1)2 + 1 = (x2 + x + 1) (x2 –x – 5) for

x Ī (–2, 3) will have number of solutions,

A

1

B

2

C

3

D

Zero

Answer

Zero

Explanation

Solution

Since x2 + x + 1 > 0 " x, dividing both sides by x2 + x + 1 we get

(x2 + x + 1) + 1(x2+x+1)\frac{1}{(x^{2} + x + 1)}= x2 – x – 5

\ L.H.S. ³ 2

But x2 – x – 5 < 1 for x Ī (–2, 3) i.e. the equation has no

solution.