\( 0<a<b<c<d \) ve \( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}=\frac{1}{4} \) olduğuna göre, a nın alabileceği kaç farklı tam sayı değeri vardır? \( \begin{array}{lllll}\text { A) } 5 & \text { B) } 6 & \text { C) } 8 & \text { D) } 9 & \text { E) } 11\end{array} \)

QS Express each of the following having a ralional denominator: \[ \frac{1}{1+\sqrt{2}+\sqrt{3}} \]

Simplify the expression using the Quotient of Powers Property: \( \frac{x^{5}}{x^{2}} \)

\( f ( x ) = \frac { x + 4 } { x - 1 } ; \quad x _ { 0 } = 0 \)

Teava le equatiaui parawetriche di \( \left\{\begin{array}{l}x+y+z=1 \\ 2 x-y-z=0\end{array}\right. \)

iii. Without expending determinant prove that \( \left|\begin{array}{ccc}\alpha & \beta \gamma & \alpha \beta \gamma \\ \beta & \gamma \alpha & \alpha \beta \gamma \\ \gamma & \alpha \beta & \alpha \beta \gamma\end{array}\right|=\left|\begin{array}{ccc}\alpha & \alpha^{2} & \alpha^{3} \\ \beta & \beta^{2} & \beta^{3} \\ \gamma & \gamma^{2} & \gamma^{3}\end{array}\right| \) v. Prove the identity \( \left\{\left[\begin{array}{ccc}1 & w & w^{2} \\ w & w^{2} & 1 \\ w^{2} & 1 & w\end{array}\right]+\left[\begin{array}{ccc}w & w^{2} & 1 \\ w^{2} & 1 & w \\ w & w^{2} & 1\end{array}\right]\right\}\left[\begin{array}{c}1 \\ w \\ w^{2}\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)