Question

Find the product of ( 1/2xcube) (-10x) (1/5xsquare) verify the result for x =1.​

Answer 1

SOLUTION :-

TO DETERMINE :-

• The product

$\displaystyle \sf{ \bigg(\frac{1}{2 {x}^{3} } \bigg) \times ( - 10x) \times \bigg( \frac{1}{5 {x}^{2} } \bigg) }$

• TO verify the result for x = 1

EVALUATION :-

DETERMINATION OF PRODUCT :-

$\displaystyle \sf{ \bigg(\frac{1}{2 {x}^{3} } \bigg) \times ( - 10x) \times \bigg( \frac{1}{5 {x}^{2} } \bigg) }$

$= \displaystyle \sf{ \bigg( - \frac{5}{ {x}^{2} } \bigg) \times \bigg( \frac{1}{5 {x}^{2} } \bigg) }$

$\displaystyle \sf{ = - \frac{1}{ {x}^{4} } }$

Therefore

$\displaystyle \sf{ \bigg(\frac{1}{2 {x}^{3} } \bigg) \times ( - 10x) \times \bigg( \frac{1}{5 {x}^{2} } \bigg) } = - \frac{1}{ {x}^{4} }$

VERIFICATION :-

For x = 1

LHS

$= \displaystyle \sf{ \bigg(\frac{1}{2 .{(1)}^{3} } \bigg) \times ( - 10.1) \times \bigg( \frac{1}{5. {(1)}^{2} } \bigg) }$

$= \displaystyle \sf{ \frac{1}{2 } \times ( - 10) \times \frac{1}{5 } }$

$= - 1$

RHS

$= \displaystyle \sf{ - \frac{1}{ {x}^{4} } }$

$= \displaystyle \sf{ - \frac{1}{ {(1)}^{4} } }$

= - 1

Therefore LHS = RHS

Hence verified

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