Question

if (a+b)=15 and ab=36 what is the value of a²+b²
a. 21
b.97
c.153
d.60
​

Answer 1

Answer:

153

Step-by-step explanation:

As per the information provided in the question, We have :

• (a + b) = 15
• ab = 36

We are asked to find the value of a²+b².

In order to find the value of a²+b², We will simplify the given equations.

⇒(a + b)² = a² + 2ab + b²

⇒15² =a² + b² + 2 × 36

⇒a² + b² = 15 × 15 – 72

⇒a² + b² = 225 – 72

⇒a² + b² = 225 – 72

⇒a² + b² = 153

∴ Hence, The value of a² + b² is 153. (Option C)

$\rule{200}2$

Learn more!

• ( a + b)² = a² + b² + 2ab
• ( a - b )² = a² + b² - 2ab
• ( a + b )² + ( a - b)² = 2a² + 2b²
• ( a + b )² - ( a - b)² = 4ab
• ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca
• a² + b² = ( a + b)² - 2ab
• (a + b )³ = a³ + b³ + 3ab ( a + b)
• ( a - b)³ = a³ - b³ - 3ab ( a - b)
• If a + b + c = 0 then a³ + b³ + c³ = 3abc.

Answer 2

Question :

If (a + b) = 15 and ab = 36 what is the value of a² + b²

To Find :

• The value of a² + b²

GivEn Data :

• (a + b) = 15

• ab = 36

Identity Used :

• a² + b² = (a + b)² - 2ab

How to do :

Using the given identity we need to put the values of (a + b) and ab then square the value of (a + b) and multiply 2 with the value of ab and at last we need to subtract 2ab from (a + b)² to get a² + b²

Solution :

Using the identity we get :

• a² + b² = (a + b)² - 2ab

• a² + b² = (15)² - 2(36)

• a² + b² = 225 - 72

• a² + b² = 153

Hence, the answer is 153

∴ Option C is correct i.e 153

Know More Identities :

• ( a + b)² = a² + b² + 2ab

• ( a - b )² = a² + b² - 2ab

• ( a + b )² + ( a - b)² = 2(a² + b²)

• ( a + b )² - ( a - b)² = 4ab

• ( a + b + c )² = a² + b² + c² + 2(ab + bc + ca)

• (a + b - c)² = a² + b² + c² + 2(ab - bc - ca)

• a² + b² = ( a + b)² - 2ab

• (a + b )³ = a³ + b³ + 3ab( a + b)

• ( a - b)³ = a³ - b³ - 3ab( a - b)

Regards

# BeBrainly