∵α,β are roots of x2−4λx+5=0 ∴α+β=4λ and αβ=5 Also, α,γ are roots of x2−(3√2+2√3)x+7+3√3λ=0,λ>0 ∴α+γ=3√2+2√3,αγ=7+3√3λ ∵α is common root ∴α2−4λα+5=0 and α2−(3√2+2√3)α+7+3√3λ=0 From (i) - (ii) : we get α=‌