Complex Numbers And Quadratic Equations question 723
Question: If $ x^{2}+y^{2}=25,\ xy=12 $ , then $ x= $ [BIT Ranchi 1992]
Options:
A) {3, 4}
B) {3, -3}
C) {3, 4, -3, -4}
D) {-3, -3}
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{2}+y^{2}=25 $ and $ xy=12 $
Þ $ x^{2}+{{( \frac{12}{x} )}^{2}}=25\Rightarrow x^{4}+144-25x^{2}=0 $
Þ $ (x^{2}-16)(x^{2}-9)=0 $
Þ $ x^{2}=16 $ and $ x^{2}=9 $
Þ $ x=\pm 4 $ and $ x=\pm 3 $ .
BETA
