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Question
The sum of a numbers and its positive square root is 6/25. Find the numbers.
Solution
Let the number be x
By the hypothesis, we have
`rArrx+sqrtx=6/25`
⇒ let us assume that x = y2, we get
`rArry^2+y=6/25`
⇒ 25𝑦2 + 25𝑦 − 6 = 0
The value of ‘y’ can be obtained by
`y=(-b+-sqrt(b^2-4ac))/(2a)`
Where a = 25, b = 25, c = −6
`rArry=(-25+-sqrt(625-600))/50`
`rArry=(-25+-35)/50`
`rArry=1/5` or `-11/10`
`x=y^2=(1/5)^2=1/25`
∴ The number x = `1/25`
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