Math, asked by bipindas2k18, 9 months ago

find the value of - p²+q² if p-q =6and p+q=14​

Answers

Answered by Anonymous
3

Solution :-

Provided :-

• p - q = 6

• p + q = 14

We have to find

• - p² + q² or - ( p² - q²)

Now as we know

• (a + b)(a - b) = a² - b²

→ (p + q)(p - q) = p² - q²

→ (6)(14) = p² - q²

→ 84 = p² - q²

So ,

→ - (p² - q²) = - (84)

→ q² - p² = -84

Answered by InfiniteSoul
1

\sf{\underline{\boxed{\bold{Given}}}}

  • p - q = 6
  • p + q = 14

\sf{\underline{\boxed{\bold{To\:find}}}}

  • p²+q²

\sf{\underline{\boxed{\bold{Solution}}}}

\sf{\underline{\boxed{\normalsize{( a + b)^2 - ( a - b)^2 = 4ab }}}}

14^2 - 6^2 = 4pq

➤4pq = 196 - 36

➤4pq = 160

 pq = \dfrac{160}{4}

➤pq = 40

\sf{\underline{\boxed{\normalsize{pq = 40  }}}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

\sf{\underline{\boxed{\normalsize{( a + b)^2 = a^2 + b^2 +2ab }}}}

 ( 14 )^2 = p^2+ q^2 + 2 \times 40

 196 = p^2+ q^2 + 80

 196 - 80 = p^2+ q^2

 p^2 + q^2 = 116

\sf{\underline{\boxed{\normalsize{p^2 + q^2 = 116  }}}}

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

_______________________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Similar questions