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Find the Q.E such that its roots are square of sum of roots and square of difference of roots of equation
222-2(p+)x+p+02=0
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ANSWER
Let the roots of the required equation be M and N
let the roots of the equation 2x²+2(p+q)x+p²+q²=0 be a and b
⇒a+b=−(p+q)
⇒ab=
2
(p
2
+q
2
)
⇒(a+b)
2
=(p+q)
2
⇒(a−b)
2
=(a+b)
2
−4ab
⇒(a−b)
2
=−(p−q)
2
we wanted the values of square of sum of the roots and square of difference of the roots
Now⇒M=(a+b)
2
=(p+q)
2
and
⇒N=(a−b)
2
=−(p−q)
2
⇒M+N=4pq
⇒MN=(p+q)
2
[−(p−q)
2
]
⇒MN=−(p
2
−q
2
)
2
hence the required equation is
⇒x
2
−(4pq)x−(p
2
−q
2
)
2
=0
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