We can prove this by contradiction. Let's assume that the equation (a^2+b^2)x^2 + 2 = 0 has real roots when a is not equal to b. Then, we can write the equation as:
(a^2+b^2)x^2 = -2
Now, let's consider the discriminant of this quadratic equation:
D = b^2 - 4ac = 0 - 4(a^2+b^2)(0)
D = -4(a^2+b^2) < 0
Since the discriminant is negative, the quadratic equation has no real roots. However, we assumed that the equation had real roots, which is a contradiction.
Therefore, we can conclude that the equation (a^2+b^2)x^2 + 2 = 0 has no real roots when a is not equal to b.
Prove that (a^2+b^2)x^2 + 2 = 0 has no real roots if a is not equal to b
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1 answer