Question

41. If the sum of two natural number is 8 and
their product is 15, find the number.
[CBSE 2012]​

Answer 1

Answer:

HOPE IT'S HELPFUL

Step-by-step explanation:

Let the first natural number be x.

Sum of two natural numbers is 8 then other natural numbers will be 8 – x.

According to question.

Product of both natural numbers = 15 ⇒ x (8 – x) = 15 ⇒ 8x – x2 =

15 ⇒ x2 – 8x + 15 = 0 ⇒

x2 – (5 + 3)x + 15 = 0 ⇒

x2 – 5x – 3x + 15 = 0 ⇒

(x2 – 5x) – (3x – 15) = 0 ⇒

x (x – 5) – 3 (x – 5) = 0 ⇒

(x – 5) (x – 3) = 0 ⇒

x – 5 = 0 or x – 3 = 0 ⇒

x = 5 or x = 3

Thus, if First natural no. = 5

then Second natural no. = 8

if First natural no. = 3 or Second natural no. = 8

Answer 2

Answer:

x=2

y=6

Step-by-step explanation:

Let the numbers are x, y

x+y=8___eq 1 xy=15

$(x + y) ^{2} = {x}^{2} + {y}^{2} + 2xy$

(8)^2=x^2+y^2+2(15)

64=x^2+y^2+30

64-30=x^2+y^2

x^2+y^2=34

$(x - y) ^{2} = {x}^{2} + {y }^{2} - 2xy$

(x-y)^2=34-2(15)

(x-y)^2=34-30

(x-y)^2=4

x-y=2_____eq 2

eq 1-eq 2

x+y-(x-y)=8-2

x+y-x+y=4

2x=4

x=2

x+y=8

2+y=8

y=6