If α and β are roots of equation x2-(6+3 log 3 2-2 log 2 3) x+(6+2√ log 2 3-3√ log 3 2)=0 then find the value of 2(α+β)-α β.

Question

If α and β are roots of equation x2-(6+3 log 3 2-2 log 2 3) x+(6+2√ log 2 3-3√ log 3 2)=0 then find the value of 2(α+β)-α β. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given equation becomes x2-5 x+6=0 and α=2, β=3 ∴ 2(α+β)-α β=2(2+3)-2 ⋅ 3=10 ⋅ 6=4

Q. If $α$ and $β$ are roots of equation $x^{2} - (6 + 3^{l o g_{3} 2} - 2^{l o g_{2} 3}) x + (6 + 2^{l o g_{2} 3} - 3^{l o g_{3} 2}) = 0$ then find the value of $2 (α + β) - α β$ .