Question

Verify the property a x ( b x c ) = (a x b) x c by taking
1) a = (7/5), b = (-9/4), c = (1/2)

2) a = 1, b = (-13/5), c = (3/5)​

Answer 1

Answer:

a×(b×c) = (a×b)×c

$1)a = \frac{7}{5} ,b = \frac{ - 9}{4},c = \frac{1}{2} \\ lhs,a \times (b \times c) \\ = \frac{7}{5} \times ( \frac{ - 9}{4} \times \frac{1}{2} ) \\ = \frac{7}{5} \times \frac{ - 9}{8} \\ = - \frac{63}{40} \\ rhs,(a \times b) \times c \\ = (\frac{7}{5} \times \frac{ - 9}{4} ) \times \frac{1}{2} \\ = \frac{ - 63}{20} \times \frac{1}{2} \\ = - \frac{ - 63}{40} \\ hence \: lhs = rhs$

$2)a = 1,b = \frac{ - 13}{5} ,c = \frac{3}{5} \\ lhs,a \times (b \times c) \\ = 1 \times ( \frac{ - 13}{5} \times \frac{3}{5} ) \\ = 1 \times \frac{ - 39}{25} \\ = \frac{ - 39}{25} \\ rhs,(a \times b) \times c \\ =( 1 \times \frac{ - 13}{5} ) \times \frac{3}{5} \\ = \frac{ - 13}{5} \times \frac{3}{5} \\ = \frac{ - 39}{25} \\ hence \: lhs = rhs$