Question

Determine rational numbers P and Q is 7 + root 5 upon 7 minus root 5 minus 7 minus root 5 upon 7 + root 5 equals to p - 7 root 5 q

Answer 1

Answer:

$p=0$

$q=\frac{1}{11}$

Step-by-step explanation:

We have,

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=p-7\sqrt{5}q$

⇒ $\frac{(7+\sqrt{5})^2-(7-\sqrt{5})^2}{(7)^2-(\sqrt{5})^2}=p-7\sqrt{5}q$

⇒ $\frac{49+5+14\sqrt{5}-49-5-14\sqrt{5}}{49-5}=p-7\sqrt{5}q$

( Since, (a±b)² = a² ± 2ab + b² )

⇒ $\frac{28\sqrt{5}}{44}=p-7\sqrt{5}q$

⇒ $\frac{7\sqrt{5}}{11}=p-7\sqrt{5}q$

⇒ $0-7\sqrt{5}(-\frac{1}{11})=p-7\sqrt{5}q$

By comparing,

We get,

$p=0$

$q=-\frac{1}{11}$

Answer 2

Answer:

p = 0

q = (-1/11)

Step-by-step explanation:

You will understand by the given photo... hope it's helpful 4 u