Question

the equation.
Find quadratic equation such that its roots are square of sum of the roots and
square of difference of the roots of equation
2x^2+2(p+q)x+p^2+q^2​

Answer 1

Answer:

$x^2-(p^2+4pq+q^2)x+2p^3q+4p^2q^2+2pq^3=0$

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To Solve : Let two roots be $x_1$ and $x_2$.

Know *1, *2

*$x_1+x_2=-(p+q)$ --- *1

*$x_1x_2=\frac{p^2+q^2}{2}$ --- *2

Square of sum of the roots = $(x_1+x_2)^2=x_1^2+2x_1x_2+x_2^2$ --- *3

`` difference of the roots = $(x_1-x_2)^2=x_1^2-2x_1x_2+x_2^2$

By adding $-4x_1x_2$ on both sides in *3

`` difference of the roots = $(x_1-x_2)^2=x_1^2-2x_1x_2+x_2^2=(x_1+x_2)^2-4x_1x_2$ --- *4

By *1 and *3

$(p+q)^2$ is the square of sum of the roots.

By *2 and *4

$(p+q)^2-(p^2+q^2)=2pq$ is the square of difference of the roots.

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Write a quadratic equation which has roots given above.

$x^2-\{(p+q)^2+2pq\}x+{2(p+q)^2pq=0$

Simplify.

∴ $x^2-(p^2+4pq+q^2)x+2p^3q+4p^2q^2+2pq^3=0$

Answer 2

Step-by-step explanation:

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