Question

Известно что x+y=7,xy=6 найдите. значение выражения x²+y²​

Answer 1

${(x + y)}^{2} = {7}^{2} = 49 = {x}^{2} + 2xy + {y}^{2} \\ 2xy = 12 \\ {x}^{2} + {y}^{2} = 49 - 12 = 37$

Answer 2

x+y=7       I²

(x+y)²=7²

X²+2xy+y²=49

X²+y²=49-2xy

X²+y²=49-2*6

X²+y²=37

Answer 3

To find the value of the expression x² + y², we can use the following formula:

(x + y)² = x² + y² + 2xy

Given that x + y = 7 and xy = 6, we can substitute these values into the formula:

(7)² = x² + y² + 2(6)

Solving for x² + y²:

49 = x² + y² + 12

Now, to find x² + y², we can isolate it on one side of the equation:

x² + y² = 49 - 12

x² + y² = 37

So, the value of the expression x² + y² is 37.