if a and b are the roots of the equation x ^2-9x+20=0 find the value of a^2+b^2+ab
Answers
Step-by-step explanation:
Sum of roots a+b=1/9
Product of roots ab=20
Solve the two equations and get a and B
The value of a²+b²+ab is 61
GIVEN :
Quadratic equation x²- 9x + 20 = 0
a and b are the roots of the given equation
TO FIND :
The value of a²+b²+ab
SOLUTION :
To find the value of a²+b²+ab
We need to know the values of a and b
Given that a and b are the roots of the equation x²- 9x + 20 = 0
To find the roots of given equation factorize x²- 9x + 20 = 0
⇒ x²- 9x + 20 = 0
Split 9x term as - 5x - 4x [ -5 × -4 = 20 ]
⇒ x²- 5x - 4x + 20 = 0
Take common x and - 4 as shown below
⇒ x(x - 5) - 4(x - 5) = 0
Take common (x-5)
⇒ (x - 5) (x - 4) = 0
⇒ x - 5 = 0 and x - 4 = 0
x = 5 and x = 4
The roots of given equation are 5 and 4
⇒ a = 5 and b = 4
a²+b²+ab = 5² + 4² + (5)(4) = 25 + 16 + 20 = 61
The value of a²+b²+ab = 61
#SPJ2