Question

For any two numbers m, n, (m + n) : (m − n) : mn = 7 : 1 : 60. find the value of 1 m : 1 n .

Answer 1

(m + n)/(m - n) = 7/1

m + n = 7m - 7n

6m - 8n = 0 eq1

Given mn = 60

m = 60/n eq2

putting m in eq1

6 × 60/n - 8n = 0

360/n - 8n = 0

$360 - 8n {}^{2} = 0$

$360 \div 8 = n {}^{2}$

$n = 3 \sqrt{5}$

put n in eq2

m = 60/n

$m = 60 \div 3 \sqrt{5}$

$m = 20 \div \sqrt{5} = 4 \sqrt{5}$

1m : 1n

$4 \sqrt{5} \div 3 \sqrt{5}$

1m : 1n = 4 : 3



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