Question

12. If
√3+1
2
find the value of 4x2 + 2x2 - 8x +7​

Answer 1

Answer:

(2x-1) = \sqrt{3} \tag {E02} [/math] [math]\text{Squaring: }(2x-1)^2 = 3 => 4x^2 - 4x + 1 = 3[/math] [math]=> 4x^2 - 4x - 2 = 0 \tag {E03}... ... If x^2 – 12 x + 33 = 0, then what is the value of (x – 4) ^2 + [1/ (x – 4) ^2]? ... 4x^3+2x^2–8x+7=4{(√3+1)/2}^3+2{( √ 3+1)/2}^2–. ... How do I find the value of x 4^x-2*5^2x+10^x=0?

Answer 2

Answer:

Given x = (√3 +1)/2

4((√3 +1)/2)^3 + 2((√3 +1)/2)^2 − 8((√3 +1)/2) + 7

Now, 4(√3 +1)^3/8 + 2(√3 +1)^2/4 − 8(√3 +1)/2 + 7

=> (√3 +1)^3/2 + (√3 +1)^2/2 − 4(√3 +1) + 7

We know that,(a + b)^n = ∑[k=0,n] C(n,k) * a^(n−k) * b^k

Hence (a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3

and (a + b)^2 = 1a^2 + 2ab + 1b^2

=> (3√3 + 9 + 3√3 +1)/2 + (3 + 2√3 +1)/2 − 4(√3 +1) + 7

=> (6√3 + 10)/2 + (2√3 +4)/2 − 4(√3 +1) + 7

=> 3√3 + 5 + √3 + 2 − 4√3 − 4 + 7 = 10

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