Question
A number exceeds its square root by 30. What is the
number?Solution
ATQ,
Let the number be 'x'.
So, x - √x = 30
On squaring both sides, we get:
(x - √x)² = 30²
⇒ x² + x - 2x√x = 900
Now, let’s simplify:
(x - 30)² = x
⇒ x² - 60x + 900 = x
⇒ x² - 61x + 900 = 0
⇒ x² - 25x - 36x + 900 = 0
⇒ x(x - 25) - 36(x - 25) = 0
⇒ (x - 36)(x - 25) = 0
So, x = 36 or x = 25
Only x = 36 satisfies the original equation
Hence, the number is 36
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