Question

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

Answer 1

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

Answer 2

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

• 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

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

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

➤$( 14 )^2 = p^2+ q^2 + 2 \times 40$

➤$196 = p^2+ q^2 + 80$

➤$196 - 80 = p^2+ q^2$

➤$p^2 + q^2 = 116$

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

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