Question

\(\left\{{}\begin{matrix}u_6+u_7=0\\2u_5^{^2}-5u_4-5u_6=-12\end{matrix}\right.\)

Answer 1

`u_6+u_7=0`

`<=>u_1+5d+u_1+6d=0`

`<=>2u_1+11d=0`

`<=>u_1=-11/2d`

`2u_5^2-5u_4-5u_6=-12`

`<=>2(u_1+4d)^2-5(u_1+3d)-5(u_1+5d)=-12`

`<=>2u_1^2+16u_1.d+32d^2-5u_1-15d-5u_1-25d=-12`

`<=>2u_1^2+16u_1.d+32d^2-10u_1-40d=-12`

`<=>121/2d^2-88d^2+32d^2+55d-40d=-12`

`<=>9/2d^2-15d+12=0`

`<=>9d^2-30d+24=0`

`<=>3d^2-10d+8=0`

`<=>[(d=2),(d=4/3):}`

`<=>[({(d=2),(u_1=-11):}),({(d=4/3),(u_1=-22/3):}):}`