Question

c) If a + b = 10 and a² + b2 = 58, find the value of a -b and a^2 - b^2
​

Answer 1

Answer:

a + b = 10

and, a² + b² = 58

So, (a+b)² = a² + b² + 2ab

10² = 58 + 2ab

100 - 58 = 2ab

42 = 2ab

Now, to find a-b :

(a-b)² = a² + b² - 2ab

(a-b)² = 58 - 42

(a-b)² = 16

a-b = √16

a-b = 4

To find a²-b² :

(a² - b²) = (a+b)(a-b)

(a² - b²) = 10 X 4 = 40.

Step-by-step explanation:

Hope it helps :)

Answer 2

EXPLANATION.

• GIVEN

a + b = 10

a^2 + b^2 = 58

To find value of ( a - b) and ( a^2 - b^2 )

according to the question,

a + b = 10 ....(1)

a^2 + b^2 = 58

Formula of ( a^2 + b^2 ) =

( a + b) ^2 - 2ab

( a + b) ^2 - 2ab = 58

put the value of ( a + b) in equation,

we get,

( 10 ) ^2 - 2ab = 58

100 - 2ab = 58

- 2ab = 58 - 100

-2ab = - 42

ab = 21 ......(2)

From equation (1) and (2) we get,

a = 21 / b [ from equation (2)]

put a = 21 / b in equation (1)

we get,

$\frac{21}{b} + b \: = 10$

$21 \: + {b}^{2} = 10b$

${b}^{2} - 10b \: + 21 = 0$

${b}^{2} - 7b \: - 3b \: + 21 = 0$

$b(b - 7) - 3(b - 7) = 0$

$(b - \: 3)(b - 7) = 0$

Therefore,

b = 3 and b = 7

put the value of b in equation (2) we get,

put b = 3 we get,

a = 21 / b = 21 / 3 = 7

a = 7

put b = 7 we get,

a = 21 / b = 21 / 7 = 3

a = 3

Therefore,

if b = 3 and a = 7 ...... (3)

if b = 7 and a = 3 ...... (4)

From equation (3) we get

1) = ( a - b) =

( 7 - 3 ) = 4

2) = ( a^2 - b^2 )

Formula of ( a^2 - b^2 )

( a - b ) ^2 + 2ab

( a - b) = 4

( 4) ^2 + 2(21)

16 + 42

58

From equation (4) we get,

1) = ( a - b) =

( 3 - 7 ) = - 4

2) = ( a^2 - b^2 )

( a - b) ^2 + 2ab

( - 4 ) ^2 + 2 ( 21)

16 + 42

58

Therefore,

both the condition value will be same

= 58