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If a = Xm + N. Yl ; B = Xn + L. Ym And C = Xl + M. Yn, Prove that : Am - N. Bn - L. Cl - M = 1 - Mathematics

Sum

If a = xm + n. yl ; b = xn + l. ym and c = xl + m. yn,

Prove that : am - n. bn - l. cl - m = 1

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Solution

a = xm + n. yl
b = xn + l. ym
c = xl + m. yn

am - n. bn - l. cl - m = 1
LHS

= am - n. bn - l. cl - m

 =  [ x( m + n ). yl ]( m - n ) . [ x( n + l ). ym ]( n - l ) . [ x( l + m ) . yn ]( l - m )

= x( m + n )( m - n ). yl( m - n ) . x( n + l )( n - l ). ym( n - l ) . x( l + m )( l - m ). yn( l - m )

= `x^( m^2 - n^2 + n^2 - l^2 + l^2 - m^2 ) . y^( lm - ln + mn - ml + nl - nm )`

= `x^0 . y^0`

= 1 
= RHS

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 9 | Page 98
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