First slide

Theory of equations

Question

The value of $\sqrt{7 + \sqrt{7 - \sqrt{7 + \sqrt{7 - ........ \propto}}}}$ is:

Moderate

A

5
B

4
C

3
D

2

Solution

Let $y = \sqrt{7 + \sqrt{7 - y}}$
             ${(y^{2} - 7)}^{2} = 7 - y$

$\Rightarrow$            $y^{4} - 14 y^{2} + y + 42 = 0$

$\Rightarrow$       $(y - 3) (y^{3} + 3 y^{2} - 5 y - 14) = 0$

$∴$                             $y = 3$

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