Question

this is maths expansion ​

Answer 1

Question :- Expand :- (x - 1/x - 2)²

Solution :-

→ (x - 1/x - 2)²

using :-

• (a - b - c)² = a² + b² + c² - 2ab + 2bc - 2ca .

putting ,

• x = a
• 1/x = b
• 2 = c

then,

→ (x)² + (1/x)² + (2)² - 2 * x * (1/x) + 2 * (1/x) * 2 - 2 * 2 * x

→ x² + 1/x² + 4 - 2 + (4/x) - 4x

→ (x² + 1/x² - 4x + 4/x + 2) (Ans.)

Learn more :-

Let a, b and c be non-zero real numbers satisfying (a³)/(b³ + c³) + (b³)/(c³ + a³) + (c³)/(a³ + b³)

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if a²+ab+b²=25

b²+bc+c²=49

c²+ca+a²=64

Then, find the value of

(a+b+c)² - 100 = __

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Answer 2

Given :   (x  - 1/x  - 2)²  

To Find : Expand

Solution:

(x  - 1/x  - 2)²  

= [ (x - 1/x) - 2]²

using (a - b)²  = a²   - 2ab  + b²

a = (x - 1/x)   , b = 2

= (x - 1/x)²  - 2 (x - 1/x)(2)   + 2²

= (x - 1/x)²  - 4x + 4/x    +  4

now again expanding  (x - 1/x)²   using  (a - b)²  = a²   - 2ab  + b²

a = x  , b = 1/x

=  x²  - 2(x)(1/x)  + (1/x)²  - 4x + 4/x    +  4

= x²  -  2  +  1/x²  - 4x + 4/x    +  4

=  x² + 1/x²  - 4x +4/x    +  2

= x²  - 4x +  4/x  + 1/x²   +  2

(x  - 1/x  - 2)²   = x²  - 4x + 4/x  + 1/x²   +  2

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