Question

if x is equal to minus 2 and Y is equal to 1 by using identity find the value of the following​

Answer 1

Answer:

3500

Step-by-step explanation:

(5y)^3+(15/y)^3

=(5.1)^3+(15/1)^3

=5^3+15^3

=125+3375

=3500

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :}}}}$

$\boxed{\bold{ \left[ 5y + \dfrac{15}{y} \right] \left[ 25 {y}^{2} - 75 + \dfrac{225}{ {y}^{2} } \right] = 125 {y}^{3} + \dfrac{3375}{ {y}^{3} } }}$

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

$(5y + \dfrac{15}{y}) (25 {y}^{2} - 75 + \dfrac{225}{ {y}^{2} })$

$25 {y}^{2} \: can \: be \: written \: as \: {(5y)}^{2} \: \: and \: \dfrac{225}{ {y}^{2} } \: can \: be \: written \: as \: { (\dfrac{15}{y}) }^{2}$

$=(5y + \dfrac{15}{ {y}^{2} })( {(5y)}^{2} - 5y \times \dfrac{15}{y} + {( \dfrac{15}{y})}^{2})$

We know that, (x + y)(x² - xy + y²) = x³ + y³

Here, $\sf{x = 5y \: and \: y = \dfrac{15}{y}}$

By substituting the values in th identity we have,

$= {(5y)}^{3} + {( \dfrac{15}{y}) }^{3}$

$= 125 {y}^{3} + \dfrac{3375}{ {y}^{3} }$

$\boxed{\bold{ \left[ 5y + \dfrac{15}{y} \right] \left[ 25 {y}^{2} - 75 + \dfrac{225}{ {y}^{2} } \right] = 125 {y}^{3} + \dfrac{3375}{ {y}^{3} } }}$

$\mathfrak{\large{\underline{\underline{Identity\:Used :-}}}}$

(x + y)(x² - xy + y²) = x³ + y³

$\mathfrak{\large{\underline{\underline{Extra\:Information :-}}}}$

What is an Identity ?

An equation is called an identity if it is satisfied by any value that replaces its variables.

$\mathfrak{\large{\underline{\underline{Some\:important\:identities : -}}}}$

1] (x + y)² = x² + y² + 2xy

2] (x - y)² = x² + y² - 2xy

3] (x + y)(x - y) = x² - y²

4] (x + a)(x + b) = x² + (a + b)x + ab