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If x = 1/(7 + 4√3) and y = 1/(7 - 4√3), then find the value of (5x2 - 7xy + 5y2)
- A963
- B956
- C967
- D958
Answer not set
Discussion 1
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CCommunity
x = 1/(7 + 4√3)
On rationalisation?
⇒ x = (7 - 4√3) / (49 - 48)
⇒ x = (7 - 4√3)
y = 1/(7 - 4√3)
On rationalisation?
⇒ y = (7 + 4√3)/(49 - 48)
⇒ y = (7 + 4√3)
(5x2 - 7xy + 5y2)
Putting the values of x and y?
⇒ [5 × (7 - 4√3)2] - 7 × (7 - 4√3) × (7 + 4√3) + [5 × (7 + 4√3)2]
⇒ [5 × (49 + 48 - 56√3)] - 7 × (49 - 48) + [5 × (49 + 48 + 56√3)]
⇒ 5 × 97 × 2 - 7
⇒ 963
On rationalisation?
⇒ x = (7 - 4√3) / (49 - 48)
⇒ x = (7 - 4√3)
y = 1/(7 - 4√3)
On rationalisation?
⇒ y = (7 + 4√3)/(49 - 48)
⇒ y = (7 + 4√3)
(5x2 - 7xy + 5y2)
Putting the values of x and y?
⇒ [5 × (7 - 4√3)2] - 7 × (7 - 4√3) × (7 + 4√3) + [5 × (7 + 4√3)2]
⇒ [5 × (49 + 48 - 56√3)] - 7 × (49 - 48) + [5 × (49 + 48 + 56√3)]
⇒ 5 × 97 × 2 - 7
⇒ 963