Show that (ax+y)x-y(ay+z)y-z(ax+z)x-z =1
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Payal Singh 8 years, 6 months ago
Question should be Show that {tex}(a^{x+y})^{x-y} .(a^{y+z})^{y-z} .(a^{z+a})^{z-a} = 1{/tex}
Taking LHS
{tex}(a^{x+y})^{x-y} .(a^{y+z})^{y-z} .(a^{z+a})^{z-a}{/tex}
Using {tex}(x^m)^n= x^{mn}{/tex}
= {tex}a^{x^2-y^2} .a^{y^2-z^2} .a^{z^2-a^2}{/tex}
= {tex}a^{x^2-y^2+y^2-z^2+z^2-a^2}{/tex}
Using {tex}(x)^m.(x)^n= (x)^{m+n}{/tex}
= a0 = 1 = RHS
Verified
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