Question

Please please answer fast ​

Answer 1

$\red\bigstar$Answer:

• x² + y² = 97

$\pink\bigstar$ Given:

• ( x - y ) = 5
• xy = 36

$\blue\bigstar$To find:

• The value of x² + y²

$\green\bigstar$ Solution:

$\star$We know that :

• (x - y)² = x² - 2xy + y²

$\star$Now :

x² + y² = x² - 2xy + y² + 2xy

$\implies$ x² + y² = (x - y)² + 2xy

So, by substituting the values of (x - y) and 2xy, we get:

x² + y² = (5)² + 2(36)

[ $\because$ (x - y) = 5 and xy = 36 ]

$\implies$ x² + y² = 25 + 72

$\implies$$\boxed{{x}^{2}+ {y}^{2} \: = \: 97}$

$\therefore$x² + y² = 97

$\red\bigstar$ Concepts Used:

• (x - y)² = x² - 2xy + y²
• Substitution of values
• Expanding of brackets

$\pink\bigstar$ Extra - Information:

$\hookrightarrow$ (a + b)² = a² + 2ab + b²

$\hookrightarrow$ a² – b² = (a + b)(a – b)

$\hookrightarrow$ (x + a)(x + b) = x² + (a + b) x + ab

$\hookrightarrow$ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

$\hookrightarrow$ (a + b)³ = a³ + b³ + 3ab (a + b)

$\hookrightarrow$ (a – b)³ = a³ – b³ – 3ab (a – b)

$\hookrightarrow$ a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

$\hookrightarrow$ If a + b + c = 0, then a³ + b³ + c³ = 3abc

Answer 2

Answer:

the above given answer is good so please follow that