Given ab = 10 and a² + b² = 30, what is the value of y in the equation y = (a + b)²?

Given ab = 10 and a² + b² = 30, what is the value of y in the equation y = (a + b)²?

• A. 40
• B. 45
• C. 50
• D. 55

Answer: (C)

To find the value of \( y \) in the equation \( y = (a + b)^2 \), we can use the relationship derived from \( ab \) and \( a^2 + b^2 \). Start with the identity: \[ (a + b)^2 = a^2 + 2ab + b^2 \] We know from the problem that \( ab = 10 \) and \( a^2 + b^2 = 30 \). Now, we can substitute these values into the equation: 1. Substitute the value of \( a^2 + b^2 \): \[ y = a^2 + b^2 + 2ab \] becomes \[ y = 30 + 2(10) \] 2. Calculate \( 2ab \): \[ 2(10) = 20 \] 3. Now combine the results: \[ y = 30 + 20 = 50 \] Thus, the value of \( y \) is 50. This aligns with the value found in the calculation and reflects the application of the formula to relate the squares

To find the value of ( y ) in the equation ( y = (a + b)^2 ), we can use the relationship derived from ( ab ) and ( a^2 + b^2 ).

Start with the identity:

[

(a + b)^2 = a^2 + 2ab + b^2

]

We know from the problem that ( ab = 10 ) and ( a^2 + b^2 = 30 ). Now, we can substitute these values into the equation:

1. Substitute the value of ( a^2 + b^2 ):

[

y = a^2 + b^2 + 2ab

]

becomes

[

y = 30 + 2(10)

]

2. Calculate ( 2ab ):

[

2(10) = 20

]

3. Now combine the results:

[

y = 30 + 20 = 50

]

Thus, the value of ( y ) is 50. This aligns with the value found in the calculation and reflects the application of the formula to relate the squares