The number of real solutions of the equation $${2^{\frac{x}{2}}} + {\left( {\sqrt 2 + 1} \right)^x} = {\left( {5 + 2\sqrt 2 } \right)^{\frac{x}{2}}}$$ is
A.
one
B.
two
C.
four
D.
infinite
Answer :
one
Solution :
$${\left( {\frac{{\sqrt 2 }}{{\sqrt {5 + 2\sqrt 2 } }}} \right)^x} + \left( {\frac{{\sqrt 2 + 1}}{{\sqrt {5 + 2\sqrt 2 } }}} \right) = 1$$ which is of the form
$${\cos ^x}\alpha + {\sin ^x}\alpha = 1;\,\,\,\therefore x = 2.$$
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