Question

if p+q=√13 and p-q=√5 then pq=?

Answer 1

Answer:

See the photo attached

Answer 2

The value of pq is 2.

Step-by-step explanation:

Given : If  $p+q=\sqrt{13}$ and $p-q=\sqrt{5}$.

To find : The value of pq ?

Solution :

Let  $p+q=\sqrt{13}$  .....(1)

and $p-q=\sqrt{5}$ ......(2)

Add equation (1) and (2),

$p+q+p-q=\sqrt{13}+\sqrt5$

$2p=\sqrt{13}+\sqrt5$

$p=\frac{\sqrt{13}+\sqrt5}{2}$

Subtract (1) and (2),

$p+q-p+q=\sqrt{13}-\sqrt5$

$2q=\sqrt{13}-\sqrt5$

$q=\frac{\sqrt{13}-\sqrt5}{2}$

Substitute the value pf p and q in $pq$,

$pq=(\frac{\sqrt{13}+\sqrt5}{2})(\frac{\sqrt{13}-\sqrt5}{2})$

Using algebraic identity, $(a+b)(a-b)=a^2-b^2$

$pq=\frac{(\sqrt{13})^2-(\sqrt5)^2}{4}$

$pq=\frac{13-5}{4}$

$pq=\frac{8}{4}$

$pq=2$

Therefore, the value of pq is 2.

#Learn more

If pq = 6 and p + q = 5, then p? + q? = ?

la) 10

(6) 11

(c) 12

D 13​

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