Question

If a²+b²=67 and ab=9 find the values of a+b and a-b

Answer 1

a+b = √85 and a-b = 7

GIVEN

a² + b² = 67

ab = 9

TO FIND

Value of a+b and a-b

SOLUTION

We can simply solve the above problem as follows;

We are given,

a² + b² = 67

And,

ab = 9

We can write a² + b² as; (a+b)² = 67

Applying the formula -

(a+b)² = a² + b² + 2ab

Therefore,

Putting the value of 'a² + b²' and 'ab' in the above equation we get;

(a + b)² = 67 + 2 × 9

= (a² + b²) = 85

= a+b = √85

Similarly,

Applying the formula,

(a-b)² = a²+ b² - 2ab

= 67 - 2× 9

= 49

= a-b = √49

= 7

Hence, a+b = √85 and a-b = 7

#Spj2

Answer 2

Answer:

The answer to the given question is the values of a+b is

$\sqrt{85}$

and a-b is

$7$

Step-by-step explanation:

Given :

a²+b²=67

ab=9

To find :

The values of a+b and a-b

Solution :

the value of

$a +b \: and \: a - b$

is obtained by the mathematical formula. The formula is

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

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

on substituting the values in the formula, we get the resultant value

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

let a+b be x, then on solving we get

${x}^{2} = 67 + 2(9) = 67 + 18$= 85

on cancelling the square, we get the value as

$( a+ b) = \sqrt{85}$

The next answer will be found by the formula

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

let a-b be y.then the answer will be

${y}^{2} = 67 - 2(9) \\ = 67 - 18 \\ = 49$

on taking the square root we get the value as

$(a - b) = 7$

Therefore, the final answer to the given question is obtained as

the values of a+b are √85 and a-b are 7.

Hence, the answer is found

# spj5

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