The sum of two numbers is 14.And the sum of the squares of these numbers is 100.Find the ratio of the numbers?

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Answer 1 · 2016-02-15T11:10:50

#3:4#

Call the numbers #x# and #y#.

We are given:

#x+y=14#

#x^2+y^2=100#

From the first equation, #y = 14-x#, which we can substitute in the second to get:

#100 = x^2+(14-x)^2= 2x^2-28x+196#

Subtract #100# from both ends to get:

#2x^2-28x+96 = 0#

Divide through by #2# to get:

#x^2-14x+48 = 0#

Find a pair of factors of #48# whose sum is #14#. The pair #6#, #8# works and we find:

#x^2-14x+48 = (x-6)(x-8)#

So #x=6# or #x=8#

Hence #(x, y) = (6, 8)# or #(8, 6)#

The ratio of the two numbers is therefore #6:8#, i.e. #3:4#