Jawab dengan cara dan penjelasan!!

Jawab dengan cara dan penjelasan!!

$displaystyle{small{boxed{tt lim_{x to infty} sqrt{{12x}^{2} + 5x - 8} - sqrt{(3x + 2)(4x - 5)} = sqrt{3}}}}$

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Penyelesaian:

$displaystyle rm lim_{x to infty} sqrt{{12x}^{2} + 5x - 8} - sqrt{(3x + 2)(4x - 5)}$

$sf= frac{12 + 0}{ sqrt{12 + 5 times 0 - 8 times 0} + sqrt{12 - 7 times 0 - 10 times 0} }$

$sf= frac{12 + 0}{ sqrt{12 + 0 - 0} + sqrt{12 - 0 - 0} }$

$sf= frac{12}{ sqrt{12} + sqrt{12} }$

$sf= frac{12}{2 sqrt{3} + 2 sqrt{3} }$

$= frac{12}{4 sqrt{3} }$

$sf= frac{3}{ sqrt{3} }$

$sf= sqrt{3}$

$displaystylelim_{x to infty } sqrt{a {x}^{2} + bx + c } - sqrt{p {x}^{2} + qx + r }$

untuk a = p, berlaku

b – q/2√a

$= small displaystylelim_{x to infty } sqrt{12{x}^{2} + 5x - 8 } - sqrt{(3x + 2)(4x - 5)}$

$= small displaystylelim_{x to infty } sqrt{12{x}^{2} + 5x - 8 } - sqrt{ {12x}^{2} - 7x - 10 }$

diperoleh

= b – q/2√a

= (5 – (-7)/2√12

= 12/2√12

= 6/√12

= 6/2√3

= 3/√3

= 3√3/3

= √3