Question

if x+y=7 and xy=10 then the value of (1/x^3+ 1/y^3) is​

Answer 1

⠀⠀ || ✪ ϙᴜᴇsᴛɪᴏɴ ✪ ||

if x+y=7 and xy=10 then the value of (1/x^3+ 1/y^3) is ?

⠀⠀ || ✪.ANSWER.✪ ||

Given:-

• x + y = 7 .............(1)
• xy = 10 ................(2)

Find:-

• value of 1/x³ + 1/y³

|| ✪.Explanation.✪ ||

we know,

★ x - y = √[(x+y)²-4xy]

So,keep value by equ(1) and equ(2)

➥ x - y = √[(7)²-4.10]

➥ x - y = √[49-40]

➥x - y = √9

➥x - y = 3 ............(3)

Add equation(1) and equation(2),

➥ 2x = 10

➥ x = 10/2

➥x = 5

Keep value in equ(1),

➥ 5 + y = 7

➥y = 7 - 5

➥ y = 2

Thus:-

• Value of x = 5
• Value of y = 2

|| ✪.verification.✪ ||

Keep value of x and y in equ(1),

➥ x + y = 7

➥ 5 + 2 = 7

➥ 7 = 7

L.H.S. = R.H.S

That's proved

Now, find

➥ 1/x³ + 1/y³

Keep value of x and y

= 1/5³ + 1/2³

= 1/125 + 1/8

= ( 8 + 125)/(125×8)

= 133/1000 [Ans]

Answer 2

⠀ ⠀⠀ ⬛⠀ ...Given...⠀⬛⠀

• x + y = 7 ____ eq 1
• x × y = 10 ____eq 2

⠀ ⠀ ⠀ ⬛⠀...To find...⠀⬛

✏ The value of $\dfrac{1}{x ^{3} } + \dfrac{1}{ {y}^{3} }$

⠀⠀ ⠀⬛⠀... Solution...⠀⬛

✏ we know that...

✰✰ x - y = √[ (x + y)² - 4xy ]

So...

keep values by eq 1 & eq 2...

✏ x - y = √[ (7)² - 4.10 ]

✏ x - y = √[ 49 - 40 ]

✏ x - y = √9

• ✏ x - y = 3 _____ eq 3...

✰✰ Now, Add equation 1 & equation 2...

✏ 2x = 10

✏ x = 10/2

• ✏ $\boxed{\red{\underline\textbf{x = 5}}}$

Substituting the value of x in eq 1...

✏ 5 + y = 7

✏ y = 7 - 5

• ✏ $\boxed{\red{\underline\textbf{y = 2}}}$

Thus...

✰✰ Value of x = 5

✰✰ Value of y = 2

Now, we have to find...

✏ $\dfrac{1}{x ^{3} } + \dfrac{1}{ {y}^{3} }$

Substituting values of x and y...

✏ $\dfrac{1}{5 ^{3} } + \dfrac{1}{ {2}^{3} }$

✏ $\dfrac{1}{125} + \dfrac{1}{ 8}$

✏ $\dfrac{8+ 125}{ 125× 8}$

✏ $\dfrac{133}{1000}$ ⠀⠀⠀

________extra________

Substituting values of x and y in equation 1...

✏ x + y = 7

✏ 5 + 2 = 7

✏ 7 = 7

L.H.S. = R.H.S

❗Hence proved❗

__________________