Question Text
Question 7 :
<span>State whether the statement is True or False.</span><div>Evaluate: $(7x+\dfrac{2}{3}y)(7x-\dfrac{2}{3}y)$ is equal to $49x^2-\dfrac{4}{9}y^2$.<br/></div>
Question 8 :
If $x + \displaystyle \frac{1}{x} = a+ b$ and $x - \displaystyle \frac{1}{x} = a - b$, then
Question 9 :
Solve: $\cfrac { { x }^{ 2 }-{ \left( y-z \right) }^{ 2 } }{ { \left( x+z \right) }^{ 2 }-{ y }^{ 2 } } +\cfrac { { y }^{ 2 }{ -\left( x-z \right) }^{ 2 } }{ { \left( x+y \right) }^{ 2 }-{ z }^{ 2 } } +\cfrac { { z }^{ 2 }{ -\left( x-y \right) }^{ 2 } }{ { \left( y+z \right) }^{ 2 }-{ x }^{ 2 } } =$
Question 10 :
<span>State whether the statement is True or False.</span><div>Evaluate: $(a+bc)(a-bc)(a^2+b^2c^2)$ is equal to $a^4-b^4c^4$.<br/></div>
Question 11 :
In the real number system, the equation<br>$\sqrt { x+3-4\sqrt { x-1 } } +\sqrt { x+8-6\sqrt { x-1 } } =1$
Question 12 :
If $x + \dfrac {1}{x} = 2$, what is the value of $x^{2} + \dfrac {1}{x^{2}}$?
Question 17 :
If the sum and difference of two numbers are 20 and 8 respectively then the difference of their squares is :
Question 19 :
The simplified value of the experession$\displaystyle \left ( a+b-c \right )^{2}+2\left ( a+b-c \right )\left ( a-b+c \right )+\left ( a-b+c \right )^{2}$ is
Question 21 :
Two numbers are such that their sum multiplied by the sum of their squares is $5500$ and their difference multiplied by the difference of the squares is $352$. Then the numbers are ?<br/>
Question 23 :
Number of real solutions of $\sqrt { 2 x - 4 } - \sqrt { x + 5 } = 1$...