Given ax + by = c and bx + ay = d, find x2 - y2
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sachin11211:
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Answered by
77
Hii..
ax+by=c---------(1)
bx+ay=d----------(2)
add equation (1)and(2)
====(ax+bx)+(by+ay)=c+d
====x(a+b)+y(a+b)=c+d
a+b(x+y))=c+d
x+y=c+d/a+b
subtract equation (2) from(1)
=======(ax-bx)-(ay-by)=c-d
=====x(a-b)-y(a-b)=c-d
====a-b(x-y)=c-d
a-b=c-d/x-y
x^2-y^2=(x+y)(x-y)
=======(c+d/a+b)(c-d/a-b)
ax+by=c---------(1)
bx+ay=d----------(2)
add equation (1)and(2)
====(ax+bx)+(by+ay)=c+d
====x(a+b)+y(a+b)=c+d
a+b(x+y))=c+d
x+y=c+d/a+b
subtract equation (2) from(1)
=======(ax-bx)-(ay-by)=c-d
=====x(a-b)-y(a-b)=c-d
====a-b(x-y)=c-d
a-b=c-d/x-y
x^2-y^2=(x+y)(x-y)
=======(c+d/a+b)(c-d/a-b)
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