Question

18. Să se rezolve ecuațiile:
a) √x + √x + 1 + √x + 4 = 3;
b) VX + 9x + 1 + √x+8 = 3;
c) √x + 1 + √x + 4 + √x + 9 = √1-x+√4 -x + √9-xi
d) Vx+1 + 3x + 8 + x + 27 = 3216- X.​

Answer 1

Răspuns:

Explicație pas cu pas:

$a)\sqrt{x} +\sqrt{x} +1+\sqrt{x} +4=3\\3\sqrt{x} +5=3|-5\\3\sqrt{x} =-2|:3\\\sqrt{x} =-\frac{2}{3} \\(\sqrt{x} )^2=(-\frac{2}{3} )^2\\x=\frac{4}{9}$

$b) \sqrt{x} +9x+1+\sqrt{x} +8=3\\2\sqrt{x} +9x+9=3|-9\\2\sqrt{x} +9x=-6|:2\\\sqrt{x} +9x=-3|:9\\\sqrt{x} +x=-\frac{1}{3} \\(\sqrt{x} +x)^2=(-\frac{1}{3} )^2\\x+x^2=\frac{1}{9} |-x\\x^2=\frac{1}{9} -x\\x=\sqrt{\frac{1}{9}-x } \\x=\frac{1}{3} -\sqrt{x}$

Nu exista solutie pentru care x∈R

$c) \sqrt{x} +1+\sqrt{x} +4+\sqrt{x} +9=\sqrt{1} -x+\sqrt{4} -x+\sqrt{9} -xi\\3\sqrt{x} +14=-x-x+6-xi\\3\sqrt{x} +14=-2x+6-xi|-14\\3\sqrt{x} =-2x-8-xi|:3\\\\\sqrt{x} =\frac{-2x-8-xi}{3} \\\\(\sqrt{x} )^2=(\frac{-2x-8-xi}{3} )^2\\\\x=\frac{-4x-64-x-1}{9} \\\\x=\frac{-5x-65}{9}$

$d) \sqrt{x} +1+3x+8+x+27=3216-x\\\sqrt{x} +36+4x=3216-x|-4x\\\sqrt{x} +36=3216-5x|-36\\\sqrt{x} =3180-5x\\(\sqrt{x} )^2=(3180-5x)^2\\x=10112400-25x|+25x\\26x=10112400|:26\\\\x=\frac{10112400}{26} \\\\x=\frac{5056200}{13}$

Succes! :)