Question

Use variables to rewrite the following sentences more formally.
5. Are there number whose square are smaller than the number itself?
6. Is there a real number whose square is equal to 1?

Answer 1

Answer:

ans 5 - there is no number whose square is smaller than the number itself because a square is such a operation where the number is multipled by the nunber itself so the square of any number cant be smaller than the number itself

ans 6. 1 is the only real number whose square is equal to 1

Answer 2

Given :  

 Are there number whose square are smaller than the number itself?

 Is there a real number whose square is equal to 1?

To Find : Write mathematically

Solution:

 Are there number whose square are smaller than the number itself

  x² < x    , x ∈ R

x² - x   <  0

=> x(x - 1) < 0

x <  0

LHS is > 0  

0 <  x  <  1

LHS is <  0

Hence x ∈ ( 0 , 1)

All real numbers between 0 and 1 are such that

square are smaller than the number itself

a real number whose square is equal to 1

=> x² = 1   , x ∈ R

=> x² - 1= 0

=>(x + 1)(x - 1) = 0

=> x = - 1 , 1

Hence { - 1 , 1}  are 2 real numbers whose square is equal to 1

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