If D and E are points on the sides AB and AC respectively of a triangle ABC such that $DE\parallel BC$ . If AD = x cm, DB = (x - 3) cm, AE = (x + 3) cm and EC = (x - 2) cm, then what is the value (in cm) of x?
1). 3
2). 3.5
3). 4
4). 4.5
If $x + \left(\frac{1}{x}\right)$ = $\sqrt{13}$, then what is the value of $x^{5} - \left(\frac{1}{x^{5}}\right)$?
1). 169
2). $169\sqrt{3}$
3). 393
4). 507
What is the difference of the factors of the expression $x^{2}+ \left(\frac{1}{x^{2}}\right) - 6$
1). 0
2). 1
3). 2
4). 4
If $\left(x-\frac{1}{3}\right)^{2}+(y-4)^{2}$ = 0 , then what is the value of $\frac{y+x}{y-x}$ ?
1). $\frac{11}{13}$
2). $\frac{13}{11}$
3). $\frac{16}{9}$
4). $\frac{9}{16}$
What is the difference of the cube and square of the common root of $(x^{2}-8x+15)=0$ and $(y^{2}+2y-35)=0$
1). 76
2). 100
3). 294
4). 318