Question

What two numbers that if multiplied equal -90 and if added equal 8?

Answer 1

`x-first\ number\\y-second\ number\\\\ \left \{ {{x\cdot\ y=-90} \atop {x+y=8}} \right.\\\\From\ second\ equayion:\\x=8-y\\\\Substracted\ to\ first\ equation:\\(8-y)y=-90\\-y^2+8y+90=0\\\\\Delta=b^2-4ac\\\Delta=8^2-4\cdot(-1)\cdot90=64+360=424\\√(\Delta)=√(424)2√(106)\\\\y_1=(-b+√(\Delta))/(2a)=(-8+2√(106))/(2\cdot(-1))=4-√(106)\\y_2=(-b-√(\Delta))/(2a)=(-8-2√(106))/(2\cdot(-1))=4+√(106)\\\\x_1=8-(4-√(106))=8-4+√(106)=4+√(106)`

`x_2=8-(4-+√(106))=8-4-√(106)=4-√(106)\\\\ \left \{ {{y=4-√(106)} \atop {x=4+√(106)}} \right.\\`