Question

If p+q=10 and pq=5,then the numerical value of p/q+q/p will be​

Answer 1

ANSWER:

• Value of the above expression = 18

GIVEN:

• p+q = 10
• pq = 5

TO FIND:

$value \: of \: (\dfrac{p}{q} + \dfrac{q}{p} )$

SOLUTION:

$= \dfrac{p}{q} + \dfrac{q}{p} \\ \\ = \dfrac{p {}^{2} + q {}^{2} }{pq} \: \: \: \: ...(i)$

Finding the value of p²+q²

=> p+q = 10.

Squaring both the sides.

=> p²+q²+2(pq) = 100

=> p²+q²+10 = 100

=> p²+q² = 90

Putting the values in (i)

$= \dfrac{90}{5} \\ \\ = 18$

Value of the above expression = 18

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

the answer is 18 .

thank you