Question

Am nevoie de ajutor cu acest exercitiu!

Answer 1

$\displaystyle 5-x,~x+7,~3x+11\\\\ x+7=\sqrt{(5-x)(3x+11)} \Rightarrow (x+7)^2=\Big(\sqrt{(5-x)(3x+11)} \Big)^2 \Rightarrow \\\\ \Rightarrow x^2+2 \cdot x \cdot 7+7^2=(5-x)(3x+11) \Rightarrow \\\\ \Rightarrow x^2+14x+49=15x+55-3x^2-11x \Rightarrow \\\\ \Rightarrow x^2+3x^2+14x-15x+11x+49-55=0 \Rightarrow 4x^2+10x-6=0\big|:2 \Rightarrow \\\\ \Rightarrow 2x^2+5x-3=0\\\\ \Delta=5^2-4 \cdot 2 \cdot (-3)=25+24=49 > 0$

$\displaystyle x_1=\frac{-5-\sqrt{49} }{2 \cdot 2}=\frac{-5-7}{4} =\frac{-12}{4} =-3\\\\ x_2=\frac{-5+\sqrt{49} }{2\cdot2} =\frac{-5+7}{4} =\frac{2}{4} =\frac{1}{2}$