Easy but Worth Trying

try this:
ac=x
bc=y

then
given condition : x³+y³=1

we have to prove: x²+y²-1> 6(1-x)(1-y)

assume x>y

for negative y, x>1 (Hope you come to the same conclusion)

so, 6(1-x)(1-y)<0
but LHS>0

so the inequality is established in this case....

now the case left for us to consider is : 0≤x≤1, 0≤y≤1.

I will leave that for u to try using my hint.