If -p- and - q - are rational numbers- then find the values of -p- and -q- given that 4-2 -3-2-3- p -6- qA- p -4 -3- q -14B- p -4 -2- q -14C- p -4 -3- q -14D- p -4 -2- q -14

The correct option is B p = 4√(2), q = 14 4 2√(3)/2+√(3) = p√(6)+q 4 2√(3)/2+√(3)×2 √(3)/2 √(3) = p√(6)+q 4(2 √(3)) 2√(3)(2 √(3))/(2)^2 (√(3))^2 = p√(6)+q 8 4 ...

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Byju's Answer

Standard IX

Mathematics

Rationalisation of Surds

If 'p' and ' ...

Question

If 'p' and 'q' are rational numbers, then find the values of 'p' and 'q' given that $\frac{4 - 2 \sqrt{3}}{2 + \sqrt{3}} = p \sqrt{6} + q$

$p = - 4 \sqrt{2}, q = 14$

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$p = - 4 \sqrt{3}, q = - 14$

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$p = 4 \sqrt{2}, q = 14$

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$p = 4 \sqrt{3}, q = 14$

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Solution

The correct option is A
$p = - 4 \sqrt{2}, q = 14$

$\frac{4 - 2 \sqrt{3}}{2 + \sqrt{3}} = p \sqrt{6} + q$

$\frac{4 - 2 \sqrt{3}}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3}}{2 - \sqrt{3}} = p \sqrt{6} + q$

$\frac{4 (2 - \sqrt{3}) - 2 \sqrt{3} (2 - \sqrt{3})}{(2)^{2} - (\sqrt{3})^{2}} = p \sqrt{6} + q$

$\frac{8 - 4 \sqrt{3} - 4 \sqrt{3} + 6}{4 - 3} = p \sqrt{6} + q$

$\frac{14 - 8 \sqrt{3}}{1} = p \sqrt{6} + q$

Comparing we get

$q = 14$ and $p \sqrt{6} = - 8 \sqrt{3}$

$p = \frac{- 8 \sqrt{3}}{\sqrt{2} \sqrt{3}}$

$= \frac{- / 8^{4} \sqrt{2}}{/ 2}$

$= - 4 \sqrt{2}$

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Similar questions

Q. If

p

and

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are rational numbers, then find

p

and

q

given that

\frac{4 + \sqrt{14}}{4 - \sqrt{14}} = p + q \sqrt{14}

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(p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2})

Q. If p = −2, q = −1 and r = 3, find the value of
(i) p² + q² − r²
(ii) 2p² − q² + 3r²
(iii) p − q − r
(iv) p³ + q³ + r³ + 3pqr
(v) 3p²q + 5pq² + 2pqr
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If one geometric mean G and two arithemtic means p and q be inserted between two numbers, then $G^{2}$ is equal to:

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If 'p' and 'q' are rational numbers, then find the values of 'p' and 'q' given that 4−2√32+√3=p√6+q

The correct option is A p=−4√2,q=14 4−2√32+√3=p√6+q 4−2√32+√3×2−√32−√3=p√6+q 4(2−√3)−2√3(2−√3)(2)2−(√3)2=p√6+q 8−4√3−4√3+64−3=p√6+q 14−8√31=p√6+q Comparing we get q=14 and p√6=−8√3 p=−8√3√2√3 =−/84√2/2 =−4√2

If 'p' and 'q' are rational numbers, then find the values of 'p' and 'q' given that $\frac{4 - 2 \sqrt{3}}{2 + \sqrt{3}} = p \sqrt{6} + q$