Q114 / 180 · COMEDK 2014 · Mathematics

The number of real roots of the equation $x^{4}+\sqrt{x^{4}+20}=22$ is

  • A
    4
  • Correct answer
    B
    2
  • C
    0
  • D
    1

Solution

Given, $x^{4}+\sqrt{x^{4}+20}=22$ Add both sides 20, we get $x^{4}+20+\sqrt{x^{4}+20}=22+20$ Let $\quad \sqrt{x^{4}+20}=y$ $\therefore \quad y^{2}+y-42=0$ $\Rightarrow \quad(y-6)(y+7)=0$ $\Rightarrow \quad y=6 \quad[y \neq-7]$ $\Rightarrow \sqrt{x^{4}+20}=6 \Rightarrow x^{4}+20=36$ $\Rightarrow \quad x^{4}=16 \Rightarrow x=\pm 2$ Hence, the number of real roots of the equation is 2 .

Hence, the correct answer is option: 'B'.

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