Question

X-y=6 xy=7 x^2 - y^2 =?

Answer 1

Ответ:48

Объяснение:х-у=6

ху=7

х=6+у=> подставляем во второе: (6+у)у=7

Получается квадратное уравнение с одной неизвестной: у^2+6у^2-7=0

Д=36+28=64=8^2

у=1

х=7

Значит х^2-у^2=49-1=48

Answer 2

To find the value of $x^2 - y^2$, you can use the given equations:

1. $x - y = 6$
2. $xy = 7$

We'll start by solving for $x$ and $y$ individually, and then use those values to find $x^2 - y^2$.

First, solve equation (1) for $x$: $x = 6 + y$

Now, substitute this expression for $x$ into equation (2): $(6 + y)y = 7$

Expand the left side of the equation: $6y + y^2 = 7$

Now, subtract 7 from both sides of the equation to isolate the $y^2$ term: $y^2 = 7 - 6y$

Next, substitute this expression for $y^2$ into $x^2 - y^2$: $x^2 - (7 - 6y)$

Now, substitute the expression for $x$ from equation (1) into the equation above: $(6 + y)^2 - (7 - 6y)$

Expand and simplify: $(36 + 12y + y^2) - 7 + 6y$

Now, combine like terms: $36 + 12y + y^2 - 7 + 6y$

Combine the constants: $36 - 7 = 29$

Combine the $y$ terms: $12y + 6y = 18y$

So, the value of $x^2 - y^2$ is $29 + 18y$.

The expression $x^2 - y^2$ cannot be further simplified without knowing the specific value of $y$. If you have the value of (y, you can substitute it into the expression to find the numerical result.