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For which of the following equations are x = 5 and x = –5 both solutions?,
(a).x2 + 25
(b).x2 - 10
(c).x2 - 25
(d).x2 + 10
We will use the concept of a quadratic equation to find the required equation.
Answer: Here x = 5, and x = -5 are both solutions of the equation (c) x2-25
Let us understand the solution with the help of the following explanation.
The given two solutions are x = 5, and x = -5.
This can be written as x - 5 = 0, and x + 5 = 0.
Further combining these two we have (x - 5)(x + 5) = 0.
Finally we have (x - 5)(x + 5) = x2 - 25.
Hence, for the solutions x = 5 and x = –5, we have the equation x2 - 25.