Question

If a+b=10 and ab=16,find the value of a²-ab+b²

Answer 1

Answer:

given, a+b = 10 , ab= 16

${a}^{2} - ab + {b}^{2}$

$= {a}^{2} + {b}^{2} - ab$

$= {(a + b)}^{2} - 2ab - ab$

$= {(a + b)}^{2} - 3ab$

$= {10}^{2} - 3 \times 16$

$= 100 - 48$

$= 52$

Answer 2

Answer :

$\bigstar \: \:\large \boxed{a^{2} - ab + b^{2} = 52} \: \: \bigstar$

Explanation :

→ Given :–

• (a+b)=10
• a×b=16

→ To Find :–

• Value of a²-ab+b² =?

→ Formula Applied :–

• (a+b)²=a²+2ab+b²

→ Solution :–

We need to Find: a²-ab+b²

We can write it as a²-ab+b²-3ab+3ab [∵ 3ab-3ab=0]

=> (a²+2ab+b²)+ ab

=> (a+b)² -3ab [ (a+b)²=a²+2ab+b² ]

=> (10)² -[3×(16)] [∵ a+b=10 and ab=16]

=> 100 - 48

=> 52

∴ Value of a²-ab+b² is 52 .