If x∗y=(x+y+1)x+xy and a∗(−1∗2)=−10, then the value of a satisfying the equation is ....
Explanation
Given the operation x∗y=(x+y+1)x+xy.
First, we calculate the value of −1∗2.
(−1∗2)=(−1+2+1)(−1)+(−1)(2)
=(2)(−1)−2
=−2−2
=−4
Next, substitute this result into the equation a∗(−1∗2)=−10, which becomes a∗(−4)=−10.
a∗(−4)=(a+(−4)+1)a+a(−4)=−10
(a−3)a−4a=−10
a2−3a−4a=−10
a2−7a+10=0
We factor the quadratic equation to find the value of a.
(a−2)(a−5)=0
a=2ora=5
Thus, the values of a that satisfy the equation are 2 or 5.