Question

x,x+7,x+8 reprezinta lungimea laturii unui triunghi dreptunghic
Aflati x

Answer 1

${x}^{2} + {(x + 7)}^{2} = {(x + 8)}^{2}$

${x}^{2} + {x}^{2} + 14x + 49 = {x}^{2} + 16x + 64$

${x}^{2} + {x}^{2} - {x}^{2} + 14x - 16x + 49 - 64 = 0$

${x}^{2} - 2x - 15 = 0$

${x}^{2} - 5x + 3x - 15 = 0$

$x(x - 5) + 3(x - 5) = 0$

$(x - 5)(x + 3) = 0$

$= > x - 5 = 0 = > x_{1} = 5$

$= > x + 3 = 0 = > x_{2} = - 3 \: nu \: convine$

$= > x = 5$