Question

split the middle term of

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$3 {x}^{2} - 2 \sqrt{6} + 2$
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$\frac{x}{2} + \frac{6}{x} = 4$
plz answer​

Answer 1

Step-by-step explanation:

(i)

Given Equation is 3x² - 2√6 + 2

= (√3x)² - 2(√3x)(√2) + (√2)²

∴ a² - 2ab + b² = (a - b)²

= (√3x - √2)²

(ii)

Given Equation is : (x/2) + (6/x) = 4

⇒ x² + 12 = 8x

⇒ x² - 8x + 12 = 0

⇒ x² - 6x - 2x + 12 = 0

⇒ x(x - 6) - 2(x - 6) = 0

⇒ (x - 2)(x - 6) = 0

⇒ x = 2,6

Hope it helps!

Answer 2

2)

$\frac{x}{2} + \frac{6}{x} = 4 \\ \frac{ {x}^{2} + 12}{2x} = 4 \\ {x }^{2} + 12 = 8x \\ {x}^{2} - 8x + 12 = 0 \\ {x}^{2} - (6 + 2)x + 12 = 0 \\ {x}^{2} -6x - 2x + 12 = 0 \\ x(x - 6) - 2(x - 6) = 0 \\ (x - 6)(x - 2) = 0 \\ x = 6.....x = 2$