Why is a/b+b/a= a^2+b^2/ab
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Answered by
75
To know the whole story of squaring a binomial, let's start from basics.
- (a + b)² = (a + b)×(a + b)
=> (a + b)² = a×(a + b) + b×(a + b)
=> (a + b)² = a² + ab + ba + b²
=> (a + b)² = a² + 2ab + b²
- Using binomial theorem:
(a + b)ⁿ = C(n,0)aⁿb° + C(n,1)aⁿ–¹.b¹ + C(n,2)aⁿ–².b²+ ……………….. + C(n,n)a°bⁿ
Thus, (a + b)² = C(2,0)a².b° + C(2,1)a¹.b¹ + C(2,2)a°.b²
=> (a + b)² = 1.a².1 + 2.a.b + 1.1.b²
=> (a + b)² = a² + 2ab + b²
Answered by
29
Answer:
(a + b)ⁿ = C(n,0)aⁿb° + C(n,1)aⁿ–¹.b¹ + C(n,2)aⁿ–².b+ C(n,n)a°bⁿ
Thus, (a + b)² = C(2,0)a².b° + C(2,1)a¹.b¹ + C(2,2)a°.b²
=> (a + b)² = 1.a².1 + 2.a.b + 1.1.b²
=> (a + b)² = a² + 2ab + b²
hope this helps you
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