Question

solve the following quadratic equation by formula method x2-2√5x+2=0

Answer 1

The coefficient of the middle term is negative, but the constant term is positive. Hence, you must look for two numbers whose sum is 25–√25 and product is 33.

The product being rational, there must be some irrational conjugate multiplication happening here. If two irrational conjugates add to 25–√25, they must be 5–√±c5±c, where cc is a number we have to determine.

Their product is 33. Therefore, (5–√)2−c2=3(5)2−c2=3. Hence, the two numbers required are 5–√±2–√5±2.

Express the middle term and the constant in terms of these numbers.

x2−25–√x+3=x2−(5–√+2–√+5–√−2–√)x+(5–√+2–√)(5–√−2–√)x2−25x+3=x2−(5+2+5−2)x+(5+2)(5−2)

⟹x2−25–√x+3=x2−(5–√+2–√)x−(5–√−2–√)x+(5–√+2–√)(5–√−2–√)⟹x2−25x+3=x2−(5+2)x−(5−2)x+(5+2)(5−2)

⟹x2−25–√x+3=x[x−(5–√+2–√)]−(5–√−2–√)[x−(5–√+2–√)]⟹x2−25x+3=x[x−(5+2)]−(5−2)[x−(5+2)]

⟹x2−25–√x+3=[x−(5–√+2–√)][x−(5–√−2–√)]

now solve it answer will out....

hope it helps u

Answer 2

Answer:

Step-by-step explanation: