Question

Find two decimal numbers whose sum is 1 and product is 0.25. answer with steps​

Answer 1

→ Let the two numbers be x and y

✯According to the conditions of the question:

x + y = 1         ___(1)

(x) (y) = 0.25 ___(2)

✯ Squaring the first equation, we get:

⇒   $(x+y)^{2}$ = 1

⇒  $x^{2} +y^{2} +2xy$ = 1    ___(3)

✯ Putting the value of (x) (y)  in (3) from (2), we get:

⇒  $x^{2} +y^{2}$ + 2 (0.25) = 1

⇒  $x^{2} +y^{2}$ + 0.50 = 1

⇒  $x^{2} +y^{2}$ = 0.50  ___(4)

✯Now, calculate $(x-y)^{2}$

⇒  $(x-y)^{2} = x^{2} +y^{2} - 2xy$

⇒  $(x-y)^{2} =$  0.50 - $2xy$                { From (4) }

⇒  $(x-y)^{2}$ = 0.50 - 2(0.25)

⇒  $(x-y)^{2}$ = 0.50 - 0.50

⇒  $(x-y)^{2}$ = 0

⇒  x - y = 0

⇒  x  = y  ____(5)

✯From (1) and (5),

⇒  2x = 1

⇒ x = $\frac{1}{2}$

⇒  y = $\frac{1}{2}$          { From (5) }

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✯ So, the two numbers are 0.5 and 0.5