Question

Como resolver a equação?

$\sqrt{x} + x = 25$

Answer 1

√x + x = 25

√x = 25 - x

(√x)² = (25 - x)²

x = 625 - 50x + x²

x² - 51x + 625 = 0

∆ = 2601 - 2500

∆ = 101

x' = (51 + √101)/2

x" = (51 - √101)/2

Porém :

√x' + x' ≠ 25 e √x" + x" = 25

Então a resposta é,

x = (51 - √101)/2

Answer 2

$\large\boxed{\boxed{\boxed{{Ol\'a}}}}}$

Respondendo:

$\sqrt{x}+x=25$

$\sqrt{x}=25-x$

$x=(25-x)^2$

$x=(25-x)(25-x)$

$x=625-25x-25x+x^2$

$x=625-50x+x^2$

$625-50x+x^2-x$

$x^2-50x-x+625$

$x^2-51x+625$

onde:

a=1 ; b =—51 e c=625

lembrando que:

$\Delta=b^2-4.a.c$

$\Delta=(-51)^2-4.1.625$

$\Delta=2601-2500$

$\Delta=101$

$x_{1},_{2}=\frac{-b±\sqrt{\Delta}}{2.a}$

$x_{1},_{2}=\frac{51±\sqrt{101}}{2.1}$

$x_{1},_{2}=\frac{51±\sqrt{101}}{2}$

:::::::Espero ter ajudado::::::::