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New problems in senior high school mathematics. How to do the sixth question
Let a 1 be a, a2 aq, a3 aqq, and q is greater than 0.

a 1+2a2-a3=0

a( 1+2q-qq)=0

qq-2q- 1=0

Q- 1 = plus or minus root number 2 Because Q is greater than 0, Q = 1+ root number 2.

A9+a 10 a times the eighth power of Q+A times the ninth power of Q QQ+QQ.

——————————— = QQ = 3+2 times the root number 2.

A7+a8 a times the 6th power of Q+A times the 7th power of Q1+Q0+Q.

Choose C.