Question Number 10206 by konen last updated on 30/Jan/17

 ^3 (√(49+^3 (√(49+^3 (√(49....)) )))) =x  (√(4(√(4(√(4(√(4....)))))))) =y  ⇒x^2 −y=?

Answered by FilupSmith last updated on 30/Jan/17

y=(√(4(√(4(√(4(√(...))))))))  y^2 =4y  y^2 −4y=0  y(y−4)=0  y=0, 4  (y=0 is illogical)  ∴ y=4  x=^3 (√(49+^3 (√(49+^3 (√(49....)) ))))  x^3 =49+x  x^3 −x−49=0  x ≈ 3.7504   (from WolframAlpha)     x^2 −y ≈ (3.7504)^2 −4  x^2 −y ≈ 14.0655−4  x^2 −y ≈ 10.0655