Question

if x^2+1/25x^2=43/5. find. x^3+1/125x^3

Answer 1

Answer:

${x}^{3} + \frac{1}{125 {x}^{3} } = ± \frac{126}{5}$

Step-by-step explanation:

If

${x}^{2} + \frac{1}{25 {x}^{2} } = \frac{43}{5}$

To find the value of

${x}^{3} + \frac{1}{125 {x}^{3} }$

First find the value of

$(x + \frac{1}{5x} ) \\ \\ for \: that \\ convert \: {x}^{2} + \frac{1}{25 {x}^{2} } \: into \: complete \: square \\ \\ {x}^{2} + 2x \frac{1}{5x} + \frac{1}{25 {x}^{2} } = \frac{43}{5} + \frac{2}{5} \\ \\ {(x + \frac{1}{5x}) }^{2} = \frac{45}{5} \\ \\ {(x + \frac{1}{5x}) }^{2} = {(3)}^{2} \\ \\ x + \frac{1}{5x} = ± 3$

So,

${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \\ \\ {x}^{3} + ({ { \frac{1}{5x} })^{3} } = (x + \frac{1}{5x} )( {x}^{2} - x( \frac{1}{5x} ) + \frac{1}{25 {x}^{2} } \\ \\ = 3( \frac{43}{5} - \frac{1}{5} ) \\ \\ = 3 \times \frac{43 - 1}{5} \\ \\ {x}^{3} + \frac{1}{125 {x}^{3} }= \frac{126}{5} \\ \\ or \\ \\ {x}^{3} + \frac{1}{125 {x}^{3} } = - \frac{126}{5}$

Hope it helps you.

Answer 2

Answer:

125/5

Step-by-step explanation:

x^2+1/25x^2=43/5

IF

x^2+2x1/5+1/25=43/5+2/5

(x+1/5x)^2=45/5

(x+1/5x)=±9

THEN

x^3+1/125x^3=(x+1/5x)[x^2-x(1/5x)+(1/25x)]

x^3+1/125x^3=3(43/5-1/5)

x^3+1/125x^3=3(42/5)

x^3+1/125x^3=3×42/5

x^3+1/125x^3=126/5

[126/5]

THANK YOU

Please like the answer