﻿ The number of real roots of the equation (x + 3)4 + (x + 5)4 = 16 is : Kaysons Education

# The Number Of Real Roots Of The Equation (x + 3)4 + (x + 5)4 = 16 Is

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## Question

### Solution

Correct option is

2

Let y = x + 4 so that given equation is (y – 1)4 + (y + 1)4 = 16

or 2(y4 + 6y2 + 1) = 16   or   y4 + 6y2 – 7 = 0

or (y2 + 7) (y2 – 1) = 0  ∴

or x + 4 = ± 1

or x = – 3, – 5 are the only two real roots.

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