Question

Х (х-2)=63; х (х+4)=77

Answer 1

$x^{2} -2x-63=0 \\ D= b^{2} -4ac= (-2)^{2} -4*1*(-63)=256 \\ x_{1} = \frac{-(-2)+ \sqrt{256} }{2*1} = \frac{4+16}{2} =10 \\ x_{2}= \frac{-(-2)- \sqrt{256} }{2*1} = \frac{4-16}{2} =-6 \\ x^{2} +4x-77=0 \\ D= b^{2} -4ac= 4^{2} -4*1*(-77)=16+308=324 \\ x_{1}= \frac{-4+ \sqrt{324}}{2*1} = 7 \\ x_{2} = \frac{-4- \sqrt{324} }{2}=-11$