Math, asked by ThePrateekYadav, 1 month ago

If x = √3+1 / 2 , then find 4x³+2x²-8x+7 .​

Answers

Answered by shreyaadu14
0

Answer:

Step-by-step explanation:

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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