Question

if a+b=2,a^3+b^3=27 then a,b are roots of the equation?

Answer 1

a3+b3+(−9)3−3ab(−9)=(a+b−9)(a2+b2−ab+9a+9b+81)=0

therefore

⎧⎩⎨a+b−9=0ora=b=−9

since a>b>0 thus

a+b−9=0

Set f(x)=ax2+bx−9. We have f(1)=a+b−9=0, thus

Q=1 and P=−9a finally

4Q−aP=4+9=13