What is the value?

Algebra Level pending

Given the equation ${ yx }^{ x } = { x }^{ yx }$ , and knowing that $y$ is the smallest value for ${ \left| y \right| }^{ 2 } - 7y + 12 = 0$ , what is the value of $x\cdot (y + 1)$ ?

{ \sqrt { 3}\cdot 3} / {2}

{3 \cdot \sqrt { -2 } }/{3}

{4 \cdot \sqrt { 3 } }/{3}

4 \cdot \sqrt { 3 }

\frac {4 \cdot \sqrt [ 3 ]{ 3 } }{ \sqrt { \dfrac { 2 }{ 3 } } }

1 solution

Vitor Curtarelli
Mar 24, 2015

Using Bhaskara, or plus-times system, we know that $y = {3, 4}$ . Using the smallest value for $y$ , we know that $y = 3$ . Replacing $y$ in the first equation ${3x}^{x} = x^{3x}$ => $3x = x^{3}$ Dividing everything for $x$ , we have $3 = x^{2}$ => $x = \sqrt{3}$ . $\sqrt{3} \cdot (3+1) = 4\cdot \sqrt{3}$

What is the value?

1 solution

0 pending reports