Question

Q28. The sum of a number and its positive square root is 6/25-. Find the num!

Answer 1

Let the Number be n^2. So

n^2 + n = 6/25, or

25 n^2 + 25 n = 6, or

25 n^2 + 25 n - 6 = 0

The Product of 25 and -6 = -150. Its Factors are +30 and -5. So we Re-write the Equation as

25 n^2 + 30 n - 5 n - 6 = 0, or

5n (5n +6) - 1*(5n + 6) = 0, or

(5n - 1)(5n +6) = 0

Therefore n = 1/5 or -6/5.

Check: 1/5 +(1/5)^2 = 1/5 + 1/25 = 6/25.

Also (-6/5) + (36/25) = (-30/25) + (36/25) = 6/25.

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