इस एक्स इक्वल टू रूट 3 प्लस वन डिवाइडेड बाय टू फाइंड द वैल्यू ऑफ एक्स क्यूब प्लस टू एक्स स्क्वायर माइनस 8 एक्स प्लस 7
Answers
Correct Question :- if x = (√3 + 1)/2 , find the value of 4x³ + 2x² - 8x + 7 ?
Solution :-
Given that,
→ x = (√3 + 1)/2
→ 2x = (√3 + 1)
→ (2x - 1) = √3
Squaring both sides
→ (2x - 1)² = (√3)²
→ 4x²- 4x + 1 = 3 . { using (a - b)² = a² + b² - 2ab. }
→ 4x² - 4x = 3 - 1
→ 4x² - 4x = 2. ------------- Eqn.(1)
→ 4x² - 4x - 2 = 0
→ 2(2x² - 2x - 1) = 0
→ 2x² - 2x - 1 = 0
→ 2x² = (2x + 1). ------------- Eqn.(2)
Now, To Find :-
→ 4x³ + 2x² - 8x + 7
→ 2x²(2x + 1) - 8x + 7
Putting value of Eqn.(2) ,
→ (2x + 1)(2x + 1) - 8x + 7
→ (2x + 1)² - 8x + 7
→ (4x² + 4x + 1) - 8x + 7 { using (a + b)² = a² + b² + 2ab. }
→ 4x² + 4x - 8x + 1 + 7
→ 4x² - 4x + 8
→ (4x² - 4x) + 8
Putting value of Eqn.(1), now,
→ 2 + 8
→ 10 (Ans.)
Hence, the value of (4x³ + 2x² - 8x + 7) is 10.
Learn More :-
if a^2+ab+b^2=25
b^2+bc+c^2=49
c^2+ca+a^2=64
Then, find the value of
(a+b+c)² - 100 = ...
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