Question

plz ans Q5- 1) with photo

Answer 1

Answer : 5 and 7

Let the two consecutive odd terms be x and x + 2.

As per your question,

(1/x) + ( 1/x + 2 ) = 12/35

35 (x + 2) + 35x = 12x( x + 2 )

35x + 70 + 35x = 12x^2 + 24x

70x +70 = 12x^2 + 24x

12x^2 - 70x + 24x - 70 = 0

12x^2 - 46x - 70 = 0

6x^2 - 23x - 35 = 0

Hence, we get

x = 5 or x = -7/6

But -7/6 isn't acceptable.

So, x = 5

x + 2 = 5 + 2

So, the two odd consecutive terms are 5 and 7.

Verification :

1/5 + 1/7 = 12/35

(7 + 5) / 7 × 5 = 12 / 35

12/35 = 12/35

Hence, the two odd consecutive terms are 5 and 7.

Answer 2

$\mathfrak{\huge{Answer:}}$

Let the two numbers be = x and x + 2

According to the question :-

$\tt{\frac{1}{x} + \frac{1}{x +2} = \frac{12}{35}}$

Solve this formed equation further

=》 $\tt{\frac{x + 2 + x}{x^{2} + 2x} = \frac{12}{35}}$

Solve it further

=》 $\tt{70x + 70 = 12x^{2} + 24x}$

Some more steps to go

=》 $\tt{12x^{2} - 46x - 70}$

Last one step

=》 $\tt{6x^{2} - 23x - 35}$

Using the quadratic formula, find the value of x :-

$\bf{Quadratic\:Formula\:= \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}}$

=》 $\bf{x = \frac{23 \pm \sqrt{529 + 840}}{12}}$

Solve this formed equation further

=》 $\bf{x = \frac{23 \pm 37}{12}}$

Solve this further

=》 $\bf{x = 5, \frac{-7}{6}}$

Now, given is that the numbers are natural numbers, thus, they'll be positive.

Therefore, only 5 is acceptable as the value of x.

x = 5

Other number = x + 2 = 5 + 2 = 7

Numbers will be = $\sf{\huge{5\:and\:7}}$