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Sol.1
⅙ and ⅕
Multiplying both the numbers with with each other's denominator.
i.e. ⅙×5 and ⅕×6
This gives us
5/30 and 6/30
Now, we will multiply these obtained number with 5.
5/30×5 and 6/30×5
25/150 and 30/150
Thus, three rational number between 25/150 and 30/150 are 26/150, 27/150 and 28/150.
Sol.2
i) 1/2+√3 = 1/2+√3 × 2-√3/2-√3= 2-√3
ii) 5/√3-√5=5/√3-√5×√3+√5/√3+√5
=5(√3+√5)/3-5
=(-5/2)(√3+√5)
Sol.3
g(x)=5+2x
x=-5/2
p(x)=x³+3x²+3x+1
p(-5/2)=(-5/2)³+3(-5/2)²+3(-5/2)+1
= -125/8+75/4-15/2+1
=-125/8+75/4-15/2+1/1
= -125+150-60+8/8
= -125+150-60+8
=-27/8
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