Question

the product of two number is 21 and the sum of their square is 58 find the numbers






please help me to do this please ​

Answer 1

Answer:

Step-by-step explanation:

Let the number be x and y

XY = 21

X²+Y² = 58

X²+Y² Can also be taken as (X + Y )²

X² + Y² + 2XY = 58

X² + Y² + 2 X 21 = 58

X² + Y² +42 = 58

X² + Y²  = 58 - 42

X² + Y²  = 16

(X + Y)² = 16

X + Y = $\sqrt{16}$ = 4

Answer 2

SOLUTION

GIVEN

The product of two number is 21

The sum of their squares is 58

TO DETERMINE

The numbers

EVALUATION

Let the required numbers are a and b

By the first condition

ab = 21 - - - - - - - (1)

By the second condition

a² + b² = 58 - - - - - (2)

Now

$\sf{ {a}^{2} + {b}^{2} = 58 }$

$\sf{ \implies {(a + b)}^{2} - 2ab = 58 }$

$\sf{ \implies {(a + b)}^{2} - 2 \times 21 = 58 }$

$\sf{ \implies {(a + b)}^{2} - 42 =58 }$

$\sf{ \implies {(a + b)}^{2} =100 }$

$\sf{ \implies {(a + b)}^{} =10 \: \: \: \: - - - (3) }$

Again

$\sf{ {a}^{2} + {b}^{2} = 58 }$

$\sf{ \implies {(a - b)}^{2} + 2ab = 58 }$

$\sf{ \implies {(a - b)}^{2} + 2 \times 21 = 58 }$

$\sf{ \implies {(a - b)}^{2} + 42 = 58 }$

$\sf{ \implies {(a - b)}^{2} = 16}$

$\sf{ \implies a - b = 4 \: \: \: \: \: \: - - - (4)}$

Adding Equation 3 and Equation 4 we get

2a = 14

⇒ a = 7

From Equation 3 we get

b = 10 - 7 = 3

FINAL ANSWER

Hence the required numbers are 7 and 3

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