Extra Questions For Class 9 Math Chapter 1 | Q9

Question 9: If x = $$frac{1}{8-\sqrt{60}}$, what is the value of x3 - 5x2 + 8x - 4? Target Centum in CBSE 10th Maths Free Online CBSE Coaching online.maxtute.com Video Explanation NCERT Solution to Class 10 Maths With Videos Explanatory Answer | Number Systems In all these questions, before plugging the value of x in the expression that has to be evaluated, rationalize x and get x expressed as a number with a rational denominator. You are likely to find a clue after completing this step that will make things easier to solve. Step 1: Rationalise $\frac{1}{8 - \sqrt{60}}$ $\frac{1}{8 - \sqrt{60}}\\$ x $\frac{8 + \sqrt{60}}{8 + \sqrt{60}}$ = $\frac{8 + \sqrt{60}}{4}$ = 2 + $\frac{\sqrt{15}}{2}$ Or x - 2 = $\frac{\sqrt{15}}{2}$ Step 2: Rewrite x3 - 5x2 + 8x - 4 Because x = 2 + $\frac{\sqrt{15}}{2}$, 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
= ${$$frac{$sqrt{15}}{2}$^3}) + ${$$frac{\sqrt{15}}{2}$^2}) = $\frac{15\sqrt{15}}{8}$ + $\frac{15}{4}$ = $\frac{15{$\sqrt{15} + 2$}}{8})

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