Question 996128
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{{{ sqrt (sqrt (x+5) +x) }}} = {{{ 5 }}}.


Square both sides. You will get


{{{ sqrt (x+5) +x }}} = {{{ 25 }}}.


{{{sqrt(x+5)}}} = {{{25-x}}},


Square both sides again. You will get


{{{x + 5}}} = {{{(25 - x)^2}}},


{{{x + 5}}} = {{{625 - 50x + x^2}}},


{{{x^2 - 51x + 620}}} = {{{0}}}.


{{{x[1]}}} = {{{20}}}, {{{x[2]}}} = {{{31}}}


<U>Check</U>. {{{x[1]}}} = {{{20}}} : &nbsp;&nbsp;{{{ sqrt (sqrt (20+5) +20) }}} = {{{ sqrt (sqrt (25) +20) }}} = {{{ sqrt (5 +20) }}} = {{{ sqrt (25) }}} = {{{5}}}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;OK!


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{x[2]}}} = {{{31}}} : &nbsp;&nbsp;{{{ sqrt (sqrt (31+5) +31) }}} = {{{ sqrt (sqrt (36) +31) }}} = {{{ sqrt (-6 +31 ) }}} = {{{ sqrt (25) }}} = {{{5}}}. &nbsp;&nbsp;&nbsp;&nbsp;It is OK, &nbsp;if you admit &nbsp;{{{sqrt(36)}}} = {{{-6}}}.