Q. 35.0( 2 Votes )
Look at this pattern
12 + (4 × 2) = 32
22 + (4 × 3) = 42
32 + (4 × 4) = 52
i) Write the next two lines.
ii) Explain the general principle using algebra.
Answer :
i) 42 + (4×5) = 62
52 + (4×6) = 72
ii) General principle,
By observing the pattern we can write a general line as:
x2 + (4× (x+1)) = ( x+2 )2
Now, let us prove this using algebra.
x2 + ( 4× (x+1)) = x2 + 4x + 4
(x+2)2 = x2 + 4x + 4 ……using , (x+y)2 = x2 + 2xy + y2
Cleary, both these terms are equal.
Hence, proved.
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Now compute the squares of these numbers in head:
10.2
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12 + (4 × 2) = 32
22 + (4 × 3) = 42
32 + (4 × 4) = 52
i) Write the next two lines.
ii) Explain the general principle using algebra.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Find an easy method to compute squares of number ending in 5.
Kerala Board Mathematics Part ILook at this pattern
12 + (4 × 2) = 32
22 + (4 × 3) = 42
32 + (4 × 4) = 52
i) Write the next two lines.
ii) Explain the general principle using algebra.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Find an easy method to compute squares of number ending in 5.
Kerala Board Mathematics Part IGiven below is a method to calculate 372?
Explain why this is correct, using algebra.
Kerala Board Mathematics Part I