Question

If p and q are rational numbers and
p√15q ? 2√3 -√5/4√3-3√5 find the value of p and q​

Answer 1

$\textbf{Given:}$

$p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}$

$\textbf{To find:}$

$\text{The values of p and q}$

$\textbf{Solution:}$

$\text{Consider,}$

$p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}$

$\text{To rationalize the denominator multiply both}$

$\text{Numerator and Denominator by 4\sqrt{3}+3\sqrt{5} }$

$p-\sqrt{15}q=\dfrac{2\sqrt{3}-\sqrt{5}}{4\sqrt{3}-3\sqrt{5}}{\times}\dfrac{4\sqrt{3}+3\sqrt{5}}{4\sqrt{3}+3\sqrt{5}}$

$p-\sqrt{15}q=\dfrac{(2\sqrt{3}-\sqrt{5})(4\sqrt{3}+3\sqrt{5})}{16(3)-9(5)}$

$p-\sqrt{15}q=\dfrac{24+6\sqrt{15}-4\sqrt{15}-15}{3}$

$p-\sqrt{15}q=\dfrac{9+2\sqrt{15}}{3}$

$p-\sqrt{15}q=3+\dfrac{2}{3}\sqrt{15}$

$\text{Comparing on bothsides we get}$

$\bf\;p=3\;\text{and}\;q=\frac{2}{3}$

$\therefore\textbf{The values of p and q are 3 and \frac{2}{3} }$

Find more:

If x = √7+ √3 and xy = 4, then x4 + y4 =​

https://brainly.in/question/16537214

Answer 2

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 =