Question

If x = 1/ 8−√60, what is the value of x3 - 5x2 + 8x - 4?

Answer 1

Step-by-step explanation:

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Answer 2

Step 1: Rationalise 18−60√

18−60√ x 8+60√8+60√

= 8+60√4 = 2 + 15√2

Or x - 2 = 15√2

Step 2: Rewrite x3 - 5x2 + 8x - 4

Because x = 2 + 15√2, try and express (x3 - 5x2 + 8x - 4) in terms of (x - 2)3, (x - 2)2 and (x - 2).

(x - 2)3 = x3 - 6x2 + 12x - 8 -------- (1)

(x - 2)2 = x2 - 4x + 4 -------- (2)

Add or subtract the two equations to check whether you get the given expression

(1) + (2) = x3 - 5x2 + 8x - 4

So, x3 - 5x2 + 8x - 4 = (x - 2)3 + (x - 2)2

= (15√2)3 + (15√2)2

= 1515√8 + 154

= 15(15√+2)8

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