Quadratic EquationHard
Question
Let $x = \frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} - \sqrt{3}},y = \frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} + \sqrt{3}}$, then the value of $x^{4} + y^{4} + (x + y)^{4}$ is equal to
Options
A.527
B.1254
C.976
D.1152
Solution
$x = \frac{5 + \sqrt{21}}{2},y = \frac{5 - \sqrt{21}}{2},x + y = 5,xy = 1$
$$\begin{matrix} x^{4} + y^{4} + (x + y)^{4} & \ = \left( x^{2} + y^{2} \right)^{2} - 2(xy)^{2} + (x + y)^{4} \\ & \ = \left\lbrack (x + y)^{2} - 2xy \right\rbrack^{2} - 2x^{2}y^{2} + (x + y)^{4} \\ & \ = (25 - 2)^{2} - 2 + 5^{4} = 1152 \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
Let α and β be the distinct roots of ax2 + bx + c = 0, then isequal to...If product of roots of the equation x2 − 3kx + 2elog k − 1 = 0 is 7, then-...Given that the equation $(x - 19)(x - 97) = p$ has real roots $\alpha$ and $\beta$. Then the minimum real root of the eq...For what value of a the sum of roots of the eqn. x2 + 2 (2 − a − a2)x − a2 = 0 is zero -...If the roots of the quadratic equation x2 + px + q = 0 are tan30o and tan15o, respectively then the value of 2 + q - p i...