Question

Is x+y=10 and xy=21 find
$2( {x}^{2} + {y}^{2} )$

Answer 1

x + y = 10

Square on both sides,

(x + y)² = 10²

x² + y² +2xy = 100

x² + y² +2(21) = 100

x² + y² +42 =100

x² + y² = 100-42

x² + y² = 58
================

Then,

x² + y² = 58

Multiply by 2 on both sides,

2(x² + y²) = 2×58

2(x² + y²) = 116


I hope this will help you


-by ABHAY

Answer 2

Hey !!!

(x + y) = 10 (given )
xy = 21 (given )

we know a formula ,

(a + b ) ² -2ab= a² + b² like that we will going to get x² + y²

let us see how ¿?

x² + y² = ( x + y) ² - 2xy

x² + y² = 10² - 2×21 [from given ]

x² + y² = 100 - 42

x² + y² = 58
hence ,

2[x² + y²] = 2× 58 = 116
Answer !!!

______________________

Hope it helps you !!!

@Rajukumar111