If p and q are rational numbers and
p√15q ? 2√3 -√5/4√3-3√5 find the value of p and q
Answers
Find more:
If x = √7+ √3 and xy = 4, then x4 + y4 =
https://brainly.in/question/16537214
Answer:
Given:
p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}p−
15
q=
4
3
−3
5
2
3
−
5
\textbf{To find:}To find:
\text{The values of p and q}The values of p and q
\textbf{Solution:}Solution:
\text{Consider,}Consider,
p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}p−
15
q=
4
3
−3
5
2
3
−
5
\text{To rationalize the denominator multiply both}To rationalize the denominator multiply both
\text{Numerator and Denominator by $4\sqrt{3}+3\sqrt{5}$}Numerator and Denominator by 4
3
+3
5
p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}{\times}\dfrac{4\sqrt{3}+3\sqrt{5}}{4\sqrt{3}+3\sqrt{5}}p−
15
q=
4
3
−3
5
2
3
−
5
×
4
3
+3
5
4
3
+3
5
p-\sqrt{15}q=\dfrac{(2\sqrt{3}-\sqrt{5})(4\sqrt{3}+3\sqrt{5})}{16(3)-9(5)}p−
15
q=
16(3)−9(5)
(2
3
−
5
)(4
3
+3
5
)
p-\sqrt{15}q=\dfrac{24+6\sqrt{15}-4\sqrt{15}-15}{3}p−
15
q=
3
24+6
15
−4
15
−15
p-\sqrt{15}q=\dfrac{9+2\sqrt{15}}{3}p−
15
q=
3
9+2
15
p-\sqrt{15}q=3+\dfrac{2}{3}\sqrt{15}p−
15
q=3+
3
2
15
\text{Comparing on bothsides we get}Comparing on bothsides we get
\bf\;p=3\;\text{and}\;q=\frac{2}{3}p=3andq=
3
2
\therefore\textbf{The values of p and q are 3 and $\frac{2}{3}$}∴The values of p and q are 3 and
3
2
Find more:
If x = √7+ √3 and xy = 4, then x4 + y4 =