Find-the-all-valid-value-of-x-x-2-4-x-4-

Question Number 172282 by BaliramSingh last updated on 25/Jun/22

F i n d t h e a l l v a l i d v a l u e o f x

x^{2} - \sqrt{4 + x} = 4

Answered by dumitrel last updated on 25/Jun/22

x^{2} - 4 ⩾ 0; x + 4 ⩾ 0

x^{2} - 4 = \sqrt{4 + x} = y

x^{2} - y = 4

y^{2} - x = 4 \Rightarrow x^{2} - y^{2} + (x - y) = 0

(x - y) (x + y + 1) = 0

x = y \Rightarrow x^{2} - x - 4 = 0 \Rightarrow x = \frac{1 + \sqrt{17}}{2}

x + y + 1 = 0 \Rightarrow x^{2} + x - 3 = 0

x = \frac{- 1 - \sqrt{13}}{2}

Commented by BaliramSingh last updated on 25/Jun/22

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