if P = Qsquare then what is the square root of P .
plz as soon as ans me
Answers
Answer:
Q
Step-by-step explanation:
Q
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Answer:
Hi...☺
Here is your answer...✌
GIVEN THAT
\begin{gathered}p = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3 } + \sqrt{2} } \: \: and\: \: q = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\\end{gathered}
p=
3
+
2
3
−
2
andq=
3
−
2
3
+
2
We know that,
(p + q)² = p² + q² + 2pq
=> (p + q)² - 2pq = p² + q²
=> p² + q² = (p + q)² - 2pq .....(1)
First we calculate
\begin{gathered}{(p + q)}^{2} = {( \frac{ \sqrt{3 } - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } + \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } )}^{2} \\ \\ = {(\frac{{ (\sqrt{3} - \sqrt{2})}^{2} + {( \sqrt{3} + \sqrt{2} )}^{2} }{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} ) } )}^{2}\\ \\ =({ \frac{3 + 2 - 2 \sqrt{6} + 3 + 2 + 2 \sqrt{6} }{ {(\sqrt{3} )}^{2} - {( \sqrt{2}) }^{2} })}^{2} \\ \\ = {(\frac{10}{3 - 2}) }^{2}= {(\frac{10}{1} )}^{2}= {10}^{2}=100\end{gathered}
(p+q)
2
=(
3
+
2
3
−
2
+
3
−
2
3
+
2
)
2
=(
(
3
+
2
)(
3
−
2
)
(
3
−
2
)
2
+(
3
+
2
)
2
) 2=)( 3 ) 2 −( 2 ) 2
3+2−2
6 +3+2+2 6 )
2 =( 3−210 )
2 =( 110 ) 2 =10
2 =100
\begin{gathered}p \times q = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ pq = 1\end{gathered}
p×q=
3+ 2
3 − 2 × 3 − 2
3 + 2
pq=1
Putting value of (p+q)² and pq in (1)
We get,
p² + q² = 100-2×1 = 100-2 = 98
=> p² + q² = 98
Step-by-step explanation: