Question

Simplify 1√3+2+2√5−√3+12−√5​

Answer 1

Answer:

Let f(x) = ax³ - 3x² + 4

and

g(x) = 2x³ - 5x + a

By remainder theorem, we know that f(x) when divided by (x-2) gives a remainder equal to f(2) i.e., p = f(2) and g(x) when divided by (x-2) gives a remainder equal to g(2), i.e, = g(2).

p - 2q = 4

\implies⟹ \sf{f(2)-2g(2)=4}f(2)−2g(2)=4

\implies⟹ \sf{[a(2)^3-3(2)^2+4]-2[2(2)^3-5(2)+a]=4}[a(2)

3

−3(2)

2

+4]−2[2(2)

3

−5(2)+a]=4

\implies⟹ \sf{(8a-12+4)-2(16-10+a)=4}(8a−12+4)−2(16−10+a)=4

\implies⟹ \sf{(8a-8)-2(a+6)=4}(8a−8)−2(a+6)=4

\implies⟹ \sf{6a-20=4}6a−20=4

\implies⟹ \sf{6a=24}6a=24

\implies⟹ a=\sf\frac{24}{6}

6

24

\implies⟹ a = \bf{4}4

Hence, the value of a is 4

Answer 2

Answer:

$14+\sqrt{5}$

Step-by-step explanation:

$=1\sqrt{3}+2+2\sqrt{5}-\sqrt{3}+12-\sqrt{5}\\\\\\= 1\sqrt{3}-\sqrt{3}+2+12+2\sqrt{5}-\sqrt{5}\\\\\\= 14+\sqrt{5}$

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