the difference of two numbers is 4 and difference of their reciprocal is 1/8 find the number
Answers
• Let one number be M
and
• Another number be N
» The difference of two numbers is 4.
A.T.Q.
=> M - N = 4
=> M = 4 + N __________ (eq 1)
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» Difference of the reciprocal of the let numbers i.e. M and N is 1/8.
A.T.Q.
=> 1/N - 1M = 1/8
=> (M - N)/MN = 1/8
Cross-multiply them
=> 8(M - N) = MN
=> 8M - 8N = MN
=> 8(4 + N) - 8N = (4 + N)N
=> 32 + 8N - 8N = 4N + N²
=> 32 = 4N + N²
=> N² + 4N - 32 = 0
=> N² + 8N - 4N - 32 = 0
=> N(N + 8) -4(N + 8) = 0
=> (N - 4) (N + 8) = 0
=> N = +4, -8 (-8 neglected)
Put value of N in (eq 1)
=> M = 4 + 4
=> M = 8
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• One number = M = 8
• Another number = N = 4
_______ [ ANSWER ]
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✡ VERIFICATION :
From above calculations we have M = 8 and N = 4
Put value of M and N in (eq 1)
=> M - N = 4
=> 8 - 4 = 4
=> 4 = 4
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