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Syllabus

^{3/2}. EvaluateQ2. Look at this pattern:

${\left(\frac{1}{2}\right)}^{2}+{\left(1\frac{1}{2}\right)}^{2}=2\frac{1}{2}2=2\times {1}^{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\left(1\frac{1}{2}\right)}^{2}+{\left(2\frac{1}{2}\right)}^{2}=8\frac{1}{2}8=2\times {2}^{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\left(2\frac{1}{2}\right)}^{2}+{\left(3\frac{1}{2}\right)}^{2}=18\frac{1}{2}18=2\times {3}^{2}$

Explain the general principle using algebra.

Q3. Some natural numbers can be written as a difference of two perfect squares in two ways. For example.

24 =7

^{2}– 5^{2}= 5^{2}– 1^{2 }32 = 9^{2}– 7^{2}= 6^{2}– 2^{2 }40 =11^{2}– 9^{2}= 7^{2}– 32i) Explain using algebra, the method of writing all multiples of 8 , starting with 24 as the difference of two perfect squares in two ways.

ii) In how many different ways can we write multiples of 16, starting with 48 as the difference of two perfect squares ?

Find (x square + y square)

^{n+2}-2^{n+1}=2^{n please solve this equation need urgently for FA - 4}4x-3-3=-4x-1 4

4x+2y

^{2 _}5x describe how the expression is obtained