If #x^2-y^2=40# and #x-y=7#, what is #x#?

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Answer 1 · 2016-09-14T10:29:10

The Soln. #x=89/14, y=-9/14#.

#x^2-y^2=40#

#rArr (x-y)(x+y)=40#

But, #x-y=7#

#:. 7(x+y)=40

# rArr x+y=40/7#, and, #x-y=7#

Adding, #2x=40/7+7=89/7#

#:. x=89/14#. This, together with, #x+y=40/7# gives,

#y=40/7-x=40/7-89/14=80/14-89/14=-9/14#.

These roots satisfy the given eqns.

Hence, the Soln. #x=89/14, y=-9/14#.

Answer 2 · 2016-09-14T10:34:41

#x = 6 5/14#

#x^2-y^2=40 or (x+y)(x-y)=40 or (x+y)*7=40 or (x+y)=40/7 (1) ; (x-y) =7(2)#Adding (1) & (2) we get #2x= 7+40/7=89/7 :. x=89/14 = 6 5/14#[Ans]