Question

Which pair of numbers match this description sum is 9 product is 8?

Answer 1

Let the two no.s be x and y

By Qn,

x+y=9
》y=9-x-----(1)

Again By Qn

xy=8
ie
x(9-x)=8
ie
$9x - {x}^{2} = 8$
ie

${x}^{2} - 9x + 8 = 0$
ie
${x}^{2} - x - 8x + 8 = 0$
ie
$x(x - 1) - 8(x - 1) = 0$
ie
$(x - 8)(x - 1) = 0$
ie
$x = 8 \: \: (or) \: x = 1$
Case (i)
x=8
y=9-x=1

Case(ii)
x=1
y=9-x=9-8=1

Thus the no.s are 8 and 1

Answer 2

Explanation:

Let the two no.s be x and y

By Qn,

x+y=9

》y=9-x-----(1)

Again By Qn

xy=8

ie

x(9-x)=8

ie

9x - {x}^{2} = 89x−x

2

=8

ie

{x}^{2} - 9x + 8 = 0x

2

−9x+8=0

ie

{x}^{2} - x - 8x + 8 = 0x

2

−x−8x+8=0

ie

x(x - 1) - 8(x - 1) = 0x(x−1)−8(x−1)=0

ie

(x - 8)(x - 1) = 0(x−8)(x−1)=0

ie

x = 8 \: \: (or) \: x = 1x=8(or)x=1

Case (i)

x=8

y=9-x=1

Case(ii)

x=1

y=9-x=9-8=1

Thus the no.s are 8 and 1