Question

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

Answer 1

a + b = 10 ... (1)

ab = 16 ... (2)

We know,

(a + b)² = a² + 2ab + b² 

Now, substituting the values of (1) and (2) in the above, we get.

=> (10)² = a² + 2*(16) + b²

=> 100 = a² + 32 + b²

=> a² + b² = 100 - 32

=> a² + b² = 68 .... (3)

Now, substituting in a² - ab + b²

=> 68 - 16

=> 52

And, substituting the value of a² + b² = 68 in a² + ab + b² 

=> 68 + 16

=> 84

Answer 2

Answer:

a + b = 10 ... (1)

ab = 16 ... (2)

We know,

(a + b)² = a² + 2ab + b² 

Now, substituting the values of (1) and (2) in the above, we get.

=> (10)² = a² + 2*(16) + b²

=> 100 = a² + 32 + b²

=> a² + b² = 100 - 32

=> a² + b² = 68 .... (3)

Now, substituting in a² - ab + b²

=> 68 - 16

=> 52

And, substituting the value of a² + b² = 68 in a² + ab + b² 

=> 68 + 16

=> 84

Step-by-step explanation: