Question

X²+y²=xy(x+y)⁴=?30 баллов

Answer 1

(x+y)⁴=( х+у) ²*( х+y) ²=

=(X²+2ху+y²)*(X²+2ху+y²)=

=( ху+2ху) ( ху+2 ху) =3ху*3ху=9( ху) ².

Answer 2

Решение.

 $\bf x^2+y^2=xy$  

Применим формулу квадрата суммы .

$\bf (x+y)^2=x^2+2xy+y^2\\\\(x+y)^4=(x+y)^2\cdot (x+y)^2=(\underbrace{x^2+y^2}_{xy}+2xy)(\underbrace{x^2+y^2}_{xy}+2xy)=\\\\=(xy+2xy)(xy+2xy)=3xy\cdot 3xy=9x^2y^2$

 

Answer 3

To find the value of x² + y² in terms of xy(x + y)⁴, we need to simplify the expression.

Let's start by expanding (x + y)⁴ using the binomial theorem: (x + y)⁴ = 1x⁴ + 4x³y + 6x²y² + 4xy³ + 1*y⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴

Now, we can substitute this expression back into the original equation x² + y² = xy(x + y)⁴: x² + y² = xy(x + y)⁴ x² + y² = xy(x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴)

Expanding further, we get: x² + y² = x⁵y + 4x⁴y² + 6x³y³ + 4x²y⁴ + xy⁵

So, xy(x + y)⁴ = x⁵y + 4x⁴y² + 6x³y³ + 4x²y⁴ + xy⁵.

Note that we cannot simplify this expression any further without knowing the specific values of x and y.