Question

class 9
polynomials
q4 5

Answer 1

i think the answer of 1 is 3√3

Answer 2

$<b>Heya mate. (^_-). Solution below.$
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(1)

[] Given, (p + 1/p)² = 3

=> (p + 1/p) = √3



[] Cubing both sides,

(p + 1/p)³ = (√3)³

=> (p + 1/p)³ = (√3 × √3 × √3)

=> (p + 1/p)³ = 3√3



♠ Let, p = a and (1/p) = b



[] Using identity : (a + b)³ = a³ + b³ + 3ab(a + b)


=> (p + 1/p)³ = p³ + 1/p³ + 3 × p × 1/p(p + 1/p)

=> (p + 1/p)³ = p³ + 1/p³ + 3(p + 1/p)

=> p³ + 1/p³ = (p + 1/p)³ - 3 (p + 1/p)

=> p³ + 1/p³ = 3√3 - 3(√3)

=> p³ + 1/p³ = 3√3 - 3√3

=> p³ + 1/p³ = 0


•°• p³ + 1/p³ = 0.
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(2)

[ (1.5)³ + (4.7)³ + (3.8)³ - 3 × 1.5 × 4.7 × 3.8] ÷ [ (1.5)² + (4.7)² + (3.8)² - (1.5 × 4.7) - (4.7 × 3.8) - (3.8 × 1.5)]


♠ Let,

1.5 = a
4.7 = b
3.8 = c


=> The question becomes,

= (a³ + b³ + c³ - 3abc)/(a² + b² + c² - ab - bc - ca)


♣ Using identity : (a³ + b³ + c³ -3abc) = (a + b + c)(a² + b² + c² - ab - bc - ca) in the numerator,


= [ (a + b + c)(a² + b² + c² - ab - bc - ca)] ÷ (a² + b² + c² - ab - bc - ca)


= (a + b + c) ... [all other get cancelled]


♪ Putting the values,

= (1.5 + 4.7 + 3.8)

= 10

•°• Your answer is 10
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$<marquee>Thank you.</marquee>$