Question 813745

√(x-3)+ √(x+5)= 4

Thanks so much in advance:)


{{{sqrt(x - 3) + sqrt(x + 5) = 4}}}


{{{sqrt(x - 3) = 4 - sqrt(x + 5)}}} ----- Subtracting {{{sqrt(x + 5)}}} from each side


{{{(sqrt(x - 3))^2 = (4 - sqrt(x + 5))^2}}} ------ Squaring both sides of equation


{{{x - 3 = 16 - 4sqrt(x + 5) - 4sqrt(x + 5) + x + 5}}}


{{{x - 3 = 16 - 8sqrt(x + 5) + x + 5}}}


{{{x - 3 = 16 + x + 5 - 8sqrt(x + 5)}}}


{{{x - 3 = 21 + x - 8sqrt(x + 5)}}}


{{{x - x - 3 - 21 = - 8sqrt(x + 5)}}}


{{{- 24 = - 8sqrt(x + 5)}}}


{{{(- 24)^2 = (- 8sqrt(x + 5))^2}}} ------ Squaring both sides of equation


{{{576 = 64(x + 5)}}}


576 = 64x + 320


64x = 576 - 320


64x = 256


{{{x = 256/64}}}, or {{{highlight_green(x = 4)}}}


You can do the check!! 


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