Question

VERIFY THE PROPERTY x.(y+z)=x.y+x.z by taking x=-3/7, y=12/13, z=-5/6

Answer 1

Step-by-step explanation:

x=-3/7, y=12/13, z=-5/6

x.(y+z)= -3/7(12/13- 5/6)

= -1/26

x.y+x.z= (-3/7 * 12/13 ) + ( -3/7 * -5/6 )

= -1/26

x.(y+z)=x.y+x.z

Answer 2

The given question is we have to verify the property

$x(y + z) = x.y + x.z$

we have to verify this property by taking

$x = \frac{ - 3}{7} \\ y = \frac{12}{13} \\ z = \frac{ - 5}{6}$

substitute these values in the above expression we get.

first solve the LHS

$x(y + z) = \frac{ - 3}{7} ( \frac{12}{13} + \frac{ - 5}{6} ) \\ \frac{ - 3}{7} ( \frac{12}{13} - \frac{5}{6} ) \\ \frac{ - 3}{7} ( \frac{72 - 65}{ 78} ) \\ \frac{ - 3}{7} ( \frac{7}{78} ) \\ \frac{ - 3}{78}$

The above obtained value is LHS

let's solve for RHS we have

$( \frac{ - 3}{7} )( \frac{12}{13} ) + ( \frac{ - 3}{7} )( \frac{ - 5}{6} ) \\ ( \frac{ - 36}{78} ) + ( \frac{15}{42} ) \\ lcm \: is \: 3822 \\ ( \frac{ - 1512 + 1365}{3822} \\ \frac{ - 147}{3822} \\ \frac{ - 3}{78} \: \: \: \: \: ( \frac{ - 147}{49} = - 3)( \frac{3822}{49} = 78)$

The above obtained value is for RHS

Therefore, LHS=RHS

Hence verified that the above expression is correct

#spj2

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