Q24 of 805 Page 257

Find six rational numbers between 3 and 4.

Since, we want six numbers, we write 1 and 2 as rational numbers with denominator 6 + 1 = 7

So, multiply in numerator and denominator by 7, we get



We know that, 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28



Hence, six rational numbers between are



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22

In a right-angled triangle, prove that the hypotenuse is the longest side.

 23

In the given figure, prove that:

x = α + β + γ


 25

If , find the values of a and b.

OR


Factorize: (5a – 7b)3 + (9c – 5a)3 + (7b – 9c)3

26

Factorize:

12(x2 + 7x)2 – 8(x2 + 7x) (2x – 1) – 15(2x – 1)2