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Show that x=1-(b/a) satisfies the equation a(a+b)x2-b(a-b)x=(a-b)2,and find the other value of x.
x=(a-b)/a, a(a+b)(a-b)2/a2 -(b(a-b)(a-b)/a)=((a-b)/a)=((a-b)/a)(a2-b2+b2-ab)=a(a-b)(a-b)/a =(a-b)2
other value = (a-b)2/(a(a+b))*(a/(a-b))= (a-b)/(a+b)
x=(a-b)/a,
a(a+b)(a-b)2/a2 -(b(a-b)(a-b)/a)=(a-b)2
=((a-b)/a)=(a-b)2
=((a-b)/a)(a2-b2+b2-ab)=(a-b)2
=a(a-b)(a-b)/a =(a-b)2
α+β=[-(-b(a-b))]/[a(a+b)]
(a-b)/a +β = [b(a-b)]/[a(a+b)]
β = (a-b)[{b/a(a+b)} - 1/a]
therefore β = (b-a)/(b+a)
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