Find-x-R-x-3-2x-3-2x-5-4-x-1-

Question Number 157805 by Huy last updated on 28/Oct/21

Find x \in R :

x^{3} - 2 x + 3 = \sqrt{2 x + 5} + 4 \sqrt{x - 1}

Answered by MJS_new last updated on 28/Oct/21

rhs defined for x ⩾ 1 and strictly increasing

lhs strictly increasing for x > \frac{\sqrt{6}}{3}

\Rightarrow only 1 solution ⩾ 1

\Rightarrow x = 2 (obvious solution 8 - 4 + 3 = \sqrt{9} + 4 \sqrt{1} = 7)

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