If $${\log _{10}}x + {\log _{10}}y \geqslant 2$$ then the smallest possible value of $$x + y$$ is
A.
10
B.
30
C.
20
D.
None of these
Answer :
20
Solution :
Here, $$xy \geqslant 100.$$ Now, $${\left( {x + y} \right)^2} = {\left( {x - y} \right)^2} + 4xy \geqslant 400 + {\left( {x - y} \right)^2} \geqslant 400$$
∴ the smallest possible value of $$x + y$$ is $$20$$ $$\left( {\because \,\,x > 0,y > 0} \right).$$
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are