Question

1. let a & b be an integer part and an decimal fraction of √7, respectively. Then the integer part of a/b is? ​

Answer 1

4<7<9⟹2<7–√<3  

a=integer part of 7–√=2

b=fractional part of 7–√=7–√−2

ab=27–√−2

=2(7–√+2)(7–√−2)(7–√+2)

=27–√+47−4

=4+27–√3

2<7–√<3⟹

4+2(2)<4+27–√<4+2(3)⟹

8<4+27–√<10⟹

4+2(2)3<ab<4+2(3)3⟹

83<ab<103⟹

223< ab<313

fractional part of ab=2 or 3.

I’m guessing that 3 is the answer.

So we need to show that ab<3 is FALSE.

ab<3⟺

4+27–√3<3⟺

4+27–√<9⟺

27–√<5⟺

28<25

Since 28<25 is FALSE, then ab<3 is FALSE.

Hence 3≤ab<313.

Hence ⌊ab⌋=3.

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