| If \[\frac{{{p}^{2}}}{{{q}^{2}}}+\frac{{{q}^{2}}}{{{p}^{2}}}=1,\] then what is the value of \[({{p}^{6}}+{{q}^{6}})?\] |
A) 0
B) 1
C) 2
D) 3
Correct Answer: A
Solution :
| \[\frac{{{p}^{2}}}{{{q}^{2}}}=\frac{{{q}^{2}}}{{{p}^{2}}}=1\]\[\Rightarrow \]\[{{p}^{4}}+{{q}^{4}}={{p}^{2}}{{q}^{2}}\] |
| \[\Rightarrow \] \[{{p}^{4}}+{{q}^{4}}-{{p}^{2}}{{q}^{2}}=0\] |
| Now, \[{{p}^{6}}+{{q}^{6}}=({{p}^{2}}+{{q}^{2}})({{p}^{4}}+{{q}^{4}}-{{p}^{2}}{{q}^{2}})\] |
| \[=({{p}^{2}}+{{q}^{2}})\cdot (0)=0\] |
You need to login to perform this action.
You will be redirected in
3 sec
