1.

If m and n are the roots of quadratic equation X square - 5 x + 3 is equal to zero then find the value of M + nwhole square + A minus nwhole square ​

Answer»

<P>Let us know the RELATION between roots and coefficients first:

We consider the following quadratic EQUATION

ax^2 + BX + c = 0

If p, q be its roots, then

  • p + q = - b/a
  • pq = c/a

Now we proceed to solve the given problem:

The given equation is

x^2 - 5x + 3 = 0

The roots are m and n. Then

  • m + n = - (- 5/1) = 5
  • mn = 3/1 = 3

Therefore, (m + n)^2 + (m - n)^2

= (m + n)^2 + (m + n)^2 - 4mn

= 2 (m + n)^2 - 4mn

= 2 (5)^2 - 4 (3)

= 2 (25) - 4 (3)

= 50 - 12 = 38

∴ (m + n)^2 + (m - n)^2 = 38

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