Question

it a²+b²=74 and ab= 35, then find a+ b​

Answer 1

Given:-

• a² + b² = 74
• ab = 35

To find:-

• a + b

Answer:-

We know that,

(a + b)² = a² + b² + 2ab

→ (a + b)² = (a² + b²) + 2(ab)

Putting the values given in the question,

→ (a + b)² = 74 + 2(35)

→ (a + b)² = 74 + 70

→ (a + b)² = 144

→ (a + b) = ±√144

→ a + b = ±12 Ans

Extra knowledge:-

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

Answer 2

Given, 

$a {}^{2} + b {}^{2} = 74$

$ab \: = 35$

We know that, 

$(a+b)2=a2+b2+2ab$

(i) By putting the given values in equation

$(a+b)2=74+2x35$

$(a+b)2=74+70$

$(a+b) \: 2=144$

$a+b=144$

$a+b= 12$

So, the value is

a+b is 12.