Question

if p=4,q=3,andr= -2,then find the value of the algebraic expression
p²+q²-r²
------------
pq+qr-pr​​

Answer 1

Given

• p = 4
• q = 3
• r = -2

___________________________

To Find

• p² + q² - r²
• pq + qr - pr

___________________________

Solution

(i) p² + q² - r²

⇒ (4)² + (3)² - (-2)²

⇒ 16 + 9 - 4

⇒ 25 - 4

⇒ 21

∴ p² + q² - r² = 21 when, p = 4, q = 3 and r = -2

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(ii) pq + qr - pr​​

⇒ (4)(3) + (3)(-2) - (4)(-2)

⇒ 12 - 6 + 8

⇒ 12 + 8 - 6

⇒ 20 - 6

⇒ 14

∴ pq + qr - pr = 14 when, p = 4, q = 3 and r = -2

___________________________

Answer 2

${\bf{Given\::}}$

• p = 4

• q = 3

• r = -2

$\\ {\bf{To\: Find\::}}$

⠀⠀❶ p² + q² - r²

⠀⠀❷ pq + qr - pr

⠀⠀❸ $\bf{\dfrac{p^2\:+\:q^2\:-\:r^2}{pq\:+\:qr\:-\:pr}}$

$\\ {\bf{Solution\::}}$

❶ p² + q² - r²

➠ 4² + 3² - (-2)²

➠ 16 + 9 - 4

➠ 25 - 4

➠ 21

❷ pq + qr - pr

➠ (4 × 3) + (3 × -2) - (4 × -2)

➠ 12 + (-6) - (-8)

➠ 12 - 6 + 8

➠ 20 - 6

➠ 14

❸ $\bf{\dfrac{p^2\:+\:q^2\:-\:r^2}{pq\:+\:qr\:-\:pr}}$

➠ $\tt{\dfrac{21}{14}}$

➠ $\bf\pink{\dfrac{3}{2}}$