Question

Heya guys✌
Plz help me out with this question☺
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Answer 1

p - q = 9

pq = 36

By p - q = 9, we find out,

p = 9 + q

Therefore,

(9 + q)q = 36

9q + q^2 = 36

q = 3

Therefore,

p = 9 + 3 = 12

(i) p + q

12 + 3 = 15

(ii) p^2 - q^2

12^2 - 3^2 = 144 - 9 = 135

Hope you found this helpful :)

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{p+q=-15}}}$

$\green{\tt{\therefore{p+q=15}}}$

$\green{\tt{\therefore{p^{2}-q^{2}=-135}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies p - q = 9 \\ \\ \tt: \implies pq = 36 \\ \\ \red{\underline \bold{To \: Find:}}\\ \tt: \implies p + q = ? \\ \\ \tt: \implies {p}^{2} - {q}^{2} = ?$

• According to given question :

$\tt: \implies p - q = 9 \\ \\ \tt: \implies p = 9 + q - - - - - (1) \\ \\ \tt: \implies pq = 36 \\ \\ \text{Putting \: value \: of \: p} \\ \tt: \implies (9 + q)q = 36 \\ \\ \tt: \implies 9q + {q}^{2} = 36 \\ \\ \tt: \implies {q}^{2} + 9q - 36 = 0 \\ \\ \tt: \implies {q}^{2} + 12q - 3q - 36 = 0 \\ \\ \tt: \implies q(q + 12) - 3(q + 12) = 0 \\ \\ \tt: \implies(q - 3)(q + 12) = 0 \\ \\ \green{\tt: \implies q = 3 \: and \: - 12} \\ \\ \text{Putting \: value \: of \: q = 3\: in \: (1)} \\ \tt: \implies p = 9 + 3 \\ \\ \green{\tt: \implies p = 12} \\ \\ \text{Putting \: value \: of \: q = - 12 \: in \: (1)} \\ \tt: \implies p = 9 - 12 \\ \\ \green{\tt: \implies p = - 3}$

$\tt \circ \: p = - 3 \: and \: q = - 12 \\ \\ \bold{For \: finding \: value} \\ \green{ \tt: \implies p + q = - 3 - 12 = - 15} \\ \\ \bold{For \: finding \:another \: value} \\ \tt: \implies {p}^{2} - {q}^{2} \\ \\ \tt: \implies (p + q)(p - q) \\ \\ \tt: \implies ( - 3 - 12)( - 3 + 12) \\ \\ \tt: \implies - 15 \times 9 \\ \\ \green{\tt: \implies - 135}$

$\tt \circ \: p = 3 \: and \: q = 12 \\ \\ \bold{for \: finding \: value} \\ \green{\tt: \implies p + q = 3 + 12 = 15 }\\ \\ \bold{For \: finding \: another \: value} \\ \tt: \implies {p}^{2} - {q}^{2} \\ \\ \tt: \implies (p + q)(p - q) \\ \\ \tt: \implies 15 \times (3 - 12) \\ \\ \tt: \implies 15 \times - 9 \\ \\ \green{\tt: \implies - 135}$