Examples with solutions for Square of sum: Data with powers and roots

Exercise #1

2x2+4xy+2y2+(x+y)2(x+y)= \frac{\sqrt{2x^2+4xy+2y^2+(x+y)^2}}{(x+y)}=

Video Solution

Answer

3 \sqrt{3}

Exercise #2

Simply the following expression:

(x+x)2 (x+\sqrt{x})^2

Video Solution

Answer

x[x+2x+1] x\lbrack x+2\sqrt{x}+1\rbrack

Exercise #3

Solve for X:

x+x=x x+\sqrt{x}=-\sqrt{x}

Video Solution

Answer

0 0

Exercise #4

Solve the following equation:

x+1×x+2=x+3 \sqrt{x+1}\times\sqrt{x+2}=x+3

Video Solution

Answer

x=73 x=-\frac{7}{3}

Exercise #5

Look at the following equation:

xx+1x+1=1 \frac{\sqrt{x}-\sqrt{x+1}}{x+1}=1

This can also be written as:

x[A(x+B)x3]=0 x[A(x+B)-x^3]=0

Calculate A and B.

Video Solution

Answer

B=1 , A=4

Exercise #6

Solve the following system of equations:

{x+y=61+6xy=9 \begin{cases} \sqrt{x}+\sqrt{y}=\sqrt{\sqrt{61}+6} \\ xy=9 \end{cases}

Video Solution

Answer

x=6122.5 x=\frac{\sqrt{61}}{2}-2.5

y=612+2.5 y=\frac{\sqrt{61}}{2}+2.5

or

x=612+2.5 x=\frac{\sqrt{61}}{2}+2.5

y=6122.5 y=\frac{\sqrt{61}}{2}-2.5

Exercise #7

Look at the following equation:

x+x+1x+1=1 \frac{\sqrt{x}+\sqrt{x+1}}{x+1}=1

The same equation can be presented as follows:

x[A(x+B)x3]=0 x[A(x+B)-x^3]=0

Calculate A and B.

Video Solution

Answer

B=1 , A=4