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प्रश्न
If x = −2 and y = 1, by using an identity find the value of the following
उत्तर
Given \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]
We shall use the identity `a^3 + b^3 = (a+b)(a^2 - ab + b^2)`,
We can rearrange the \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]as
` = (5y + 15/y)[(5y)^2 + (15/y)^2 - (5y) (15/y)]`
` = (5y)^3 + (15/y)^3`
` = (5y) xx (5y) xx (5y) + (15/y) xx (15/y) xx (15/y)`
` = 125y^3 + 3375/y^3`
Now substituting the value y = 1in `125y^3 + 3375/y^3`
` = 125y^3 + 3375/y^3`
`= 125(1)^3 + 3375/(1)^3`
`= 125 + 3375`
` = 3500`
Hence the Product value of \[\left( 5y + \frac{15}{y} \right) \left( 25 y^2 - 75 + \frac{225}{y^2} \right)\]is 3500.
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