Question

Cat este x din relatiax(x+1)+(x+1)(x+2)=98

Answer 1

Răspuns:

$x^2+x + {x}^{2} + 2x + x + 2 = 98 \\ 2{x}^{2} + 4x + 2 - 98 = 0 \\ delta = {b}^{2} - 4ac = {4}^{2} - 8 \times ( - 96) = 16 + 768 = 784 \\ x1 = \frac{ - b + \sqrt{delta} }{2a} = \frac{ - 4+ \sqrt{784} }{2} =24/4=6 \\ x2 = \frac{ - 4- \sqrt{784} }{2} =-32/4=-8$

x={-8;6}

Answer 2

$x(x+1)+(x+1)(x+2)=98\Rightarrow(x+1)(x+x+2)=98\Rightarrow(x+1)(2x+2)=98\Rightarrow \\ \\ \Rightarrow (x+1)\cdot2\cdot(x+1)=98|_{:2} \Rightarrow (x+1)^2=49 \Rightarrow \sqrt{(x+1)^2}=\sqrt{49} \Rightarrow \\ \\ \Rightarrow |x+1|=7 \Rightarrow x+1=\pm7 \Rightarrow x+1\in\{-7,\ 7\}|_{-1} \Rightarrow x\in\{-8,\ \ 6\}$