Question

. If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab?​

Answer 1

Solution

Given :-

• Equation, x² - 9x + 20 = 0
• a & b are roots this Equation

Find :-

• Value of a² + b² + ab

Explanation

Using Formula

★Sum of roots = -(Coefficient of x)/(Coefficient of x²)

★Product of roots = ( constant part)/(coefficient of x²)

So,

==> Sum of roots =. -(-9)

==> a + b = 9_________(1)

And,

== > a. b = 20_________(2)

Squaring both side of equ (1)

==> (a + b )² = 9²

==> a² + b² + 2ab = 81________(3)

subtract equ(2) & equ(3)

==> a² + b² + ab = 61

Hence

• Value of a² + b² + ab will be = 61

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