The diffrence between two positive number is 7 and
square of their Sum is 289 find the two numbers?
Answers
Let two positive no. are x and x+7
(x+x+7)^2 = 289
2x + 7 = √289
2x + 7 = 17
2x = 17-7
2x = 10
x = 5
So, two no are 5 and 5+7 =12. (Answer)
» The diffrence between two positive number is 7.
• Let one number be M and another be N.
A.T.Q.
=> M - N = 7
=> M = 7 + N _______ (eq 1)
» Square of their (let numbers) sum is 289.
=> M² + N² = 289
=> (7 + N)² + N² = 289
(a + b)² = a² + b² + 2ab
=> (7)² + N² + 2(7)(N) + N² = 289
=> 49 + 2N² + 14N = 289
=> 2N² + 14N - 240 = 0
=> N² + 7N² - 120 = 0
=> N² + 15N - 8N - 120 = 0
=> N(N + 15) -8(N + 15) = 0
=> (N - 8) (N + 15) = 0
=> N = +8, -15 (-15 neglected because number can never be negative)
Put value of N in (eq 1)
=> M = 7 + 8
=> M = 15
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Sum of numbers = M + N = 15 + 8 = 23
_________ [ ANSWER ]
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✡ VERIFICATION :
We have M - N = 7
From above calculations we have M = 15 and N = 8
→ M - N = 7
→ 15 - 8 = 7
→ 7 = 7
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