Question

Question #199cc

Answer 1

100.

Explanation:

`p + q = 12`

`rArr (p+q)^2 = 144` [Squaring both sides]
`rArr p^2 + 2pq + q^2 = 144` [Expanding `(p + q)^2`]
`rArr p^2 + q^2 + 2 * 22 = 144` [As `pq = 22`]
`rArr p^2 + q^2 = 144 - 44`
`rArr p^2 + q^2 = 100`

Hence explained.

Answer 2

The answer is `=100`

Explanation:

Reminder :

`(a+b)^2=a^2+b^2+2ab`

Therefore,

`(p+q)^2=p^2+q^2+2pq`

`p^2+q^2=(p+q)^2-2pq`

`(p+q)=12`

`pq=22`

So,

`p^2+q^2=12^2-2*22=144-44=100`

Answer 3

`p^2+q^2=100`

Explanation:

`(p+q)^2=p^2+2pq+q^2`

`rArrp^2+q^2=(p+q)^2-2pq`

`color(white)(xxxxxxxx)=12^2-(2xx22)`

`color(white)(xxxxxxxx)=144-44=100`

Answer 4

`p^2 + q^2 = 100`

Explanation:

The following are give

1. `p+q=12`
2. `pq=22`

In 1. square both sides
this gives us
`(p+q)^2` `=12^2`
`p^2 + q^2 + 2pq= 144` `color(white)(xxxxxx)` `-"equation"3`

In 2. multiply both sides by 2 , this gives `2pq=44`

subtract this result from equation 3 .
this gives us
`p^2 + q^2 + 2pq -` `color(green)(2pq)` `= 144- color(green)(44)`
`p^2 + q^2 = 100`