Quadratic EquationHard
Question
The value of maximum real root minus the minimum real root of the equation $\left( x^{2} - 5 \right)^{4} + \left( x^{2} - 7 \right)^{4} = 16$ is
Options
A.$\sqrt{5} + \sqrt{7}$
B.$2\sqrt{5}$
C.$\sqrt{28}$
D.$4\sqrt{2}$
Solution
Put $x^{2} - 6 = t$
$$\begin{matrix} & & (t + 1)^{4} + (t - 1)^{4} & = 16 \\ \Rightarrow & t^{4} + 6t^{2} - 7 & & = 0 = \left( t^{2} + 7 \right)\left( t^{2} - 1 \right) \\ \Rightarrow & x^{2} - 6 & & = \pm 1 \\ \Rightarrow & x & & = \pm \sqrt{7}, \pm \sqrt{5} \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
The number of points in (- ∞,∞), for which x2 - xsinx - cosx = 0, is...Let $\alpha$ and $\beta$ be the roots of equation $x^{2} + 2ax + (3a + 10) = 0$ such that $\alpha < 1 < \beta$. Th...The largest interval for which x12 - x9 + x4 - x +1 > 0 is...Let $f(x) = x^{3} - 3x + b$ and $g(x) = x^{2} + bx - 3$, where b is a real number. If the equations $f(x) = 0$ and $g(x)...If the roots of the equation are equal in magnitude but opposite in sign, then their product is -...