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Question
If a and b are distinct real numbers, show that the quadratic equations
`2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots.
Solution
The given equation is `2(a^2+b^2)x^2+(a+b)x+1=0`
∴`D=[2(a+b)]^2-4xx2(a^2+b^2)xx1`
=`4(a^+2ab+b^2)-8(a^+b^2)`
=`4a^2+8ab+4b^2-8a^2-8b^2`
=`-4a^2+8ab-4b^2`
=`-4(a^2-2ab+b^2)`
=`-4(a-b)^2<0`
Hence, the given equation has no real roots.
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