Answer:
see explanation
Step-by-step explanation:
(a)
[tex]\frac{5}{a}[/tex] + [tex]\frac{3}{b}[/tex] + [tex]\frac{7}{c}[/tex] = 0 ( multiply through by abc to clear the fractions )
5bc + 3ac + 7ab = 0 ( subtract 5bc from both sides )
3ac + 7ab = - 5bc ( factor a out of each term on the left side )
a(3c + 7b) = - 5bc ← divide both sides by (3c + 7b)
a = - [tex]\frac{5bc}{3c+7b}[/tex]
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(b)
p = [tex]\frac{\sqrt{4r(q^2-s)} }{q}[/tex] ( multiply both sides by q )
pq = [tex]\sqrt{4r(q^2-s)}[/tex] ← square both sides
(pq)² = 4r(q² - s) ← distribute
p²q² = 4rq² - 4rs ← subtract 4rq² from both sides
p²q² - 4rq² = - 4rs ( multiply through by - 1 )
4rq² - p²q² = 4rs ← factor out q² from each term on the left side
q²(4r - p²) = 4rs ← divide both sides by (4r - p²)
q² = [tex]\frac{4rs}{4r-p^2}[/tex] ( take the square root of both sides )
q = ± [tex]\sqrt{\frac{4rs}{4r-p^2} }[/tex]
