x3 + y3 = 22 మరియు x + y = 5, అయితే x4 + y4 విలువ ఎంత?

  1. 127
  2. 222
  3. 33
  4. 800

Answer (Detailed Solution Below)

Option 3 : 33
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Detailed Solution

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x3 + y3 = (x + y)(x2 + y2 – xy) అని మనకు తెలుసు

x3 + y3 = 22 మరియు x + y = 5 అని ఇచ్చారు

⇒ 22 = 5(x2 + y2 – xy)

⇒ 22 = 5[(x + y)2 − 3xy)]

⇒ 22 = 5[(5)2 − 3xy)]

⇒ xy = 103/15

x3 + y3 = 22ను  x + y = 5తో గుణించగా,

⇒ x4 + y4 + xy(x2 + y2) = 110

⇒ x4 + y4 = 110 – xy{(x2 + y2 − 2xy + 2xy)}

⇒ x4 + y4 = 110 – xy{(x + y)2 − 2xy}

xy = 103/15 మరియు x + y = 5

⇒ x4 + y4 = 110 – 103/15{(5)2 − 2 × 103/15}

⇒ x4 + y4 = 110 – 6.87{(25 –  13.73}

⇒ x4 + y= 110 – 6.87 {(11.27)}

⇒ x4 + y4 = 110 – 77.42

⇒ x4 + y= 32.58

∴ x4 + y4  విలువ 33.

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