Question

If p = x^m+n.y^l, q = x^n+l.y^m an and r = x^l+m.y^n”, prove that
p^m-n.q^n-1.p^l-m = 1​

Answer 1

Solution :

• p = x^(m + n) . y^l

• q = x^( n + l) . y^m

• r = x^( l + m) . y^n

p^( m - n )

> [ x^(m + n) . y^l ]^( m - n )

> x^[ m² - n² ] . y^[ lm - ln ]

q^ ( n - l)

> [ x^( n + l) . y^m ] ^ ( n - l)

> x^[ n² - l² ] . y^[ mn - ml ]

r^( l - m )

> [ x^( l + m) . y^n ]^ ( l - m)

> x^[ l² - m² ] . y^ [ nl - nm ]

p^( m - n ) × q^(n - l) × r^( l - m )

> > x^[ m² - n² ] . y^[ lm - ln ] × x^[ n² - l² ] . y^[ mn - ml ] × x^[ l² - m² ] . y^ [ nl - nm ]

> x^0 y^0

> 1

Hence Proved

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