Question

Evaluate using suitable identity :( 0.7x0.7x0.7 + 0.3x0.3x0.3) / (0.7x0.7 + 0.3 x0.3 - 0.7x0.3 )

Answer 1

Answer:

make squares and cubes and then take common factors and use identity

Answer 2

The value of the expression ( 0.7 x 0.7 x 0.7 + 0.3 x 0.3 x 0.3 ) / ( 0.7 x 0.7 + 0.3 x 0.3 - 0.7 x 0.3 ) is  1.

Given: The expression,

( 0.7 x 0.7 x 0.7 + 0.3 x 0.3 x 0.3 ) / ( 0.7 x 0.7 + 0.3 x 0.3 - 0.7 x 0.3 ).

To Find: The value of the expression ( 0.7 x 0.7 x 0.7 + 0.3 x 0.3 x 0.3 ) / ( 0.7 x 0.7 + 0.3 x 0.3 - 0.7 x 0.3 )

Solution:

In this question, we shall use the identity which states that,

                 a³ + b³ = ( a + b ) × ( a² - ab + b² )                                 ...(1)

Where a and b are integer values.

Coming to the numerical, we are required to find the value of the expression,

( 0.7 x 0.7 x 0.7 + 0.3 x 0.3 x 0.3 ) / ( 0.7 x 0.7 + 0.3 x 0.3 - 0.7 x 0.3 )

If we say that a = 0.7 and b = 0.3, then we can rewrite the expression as,

             ( a³ + b³ ) / ( a² + b² - ab )                                                   ....(2)

Now, from (1), we can that;

              a³ + b³ = ( a + b ) × ( a² - ab + b² )  

Putting (1) in the numerator of (2), we get;

              ( a³ + b³ ) / ( a² + b² - ab )  

          ⇒ [ ( a + b ) × ( a² - ab + b² ) ] / ( a² + b² - ab )  

          ⇒  ( a + b )                                                                               ...(3)

Putting values a =  0.7 and b = 0.3 in (3), we get;

          ⇒  ( 0.7 + 0.3 )

          ⇒  1

Hence, the value of the expression ( 0.7 x 0.7 x 0.7 + 0.3 x 0.3 x 0.3 ) / ( 0.7 x 0.7 + 0.3 x 0.3 - 0.7 x 0.3 ) is 1.

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