Question

the sum of the reciprocal of two consecutive odd numbers is 12/35.find those numbers

Answer 1

Hey mate here is your answer ⤵⤵⤵⤵

$\sf Let\:the\:two\:consecutive\:odd\:numbers \\ \\ \sf be\:x\:and\:(x+2). \\ \\ \sf A/Q, \\ \\ \sf \: \: \: \dfrac{1}{x}+\dfrac{1}{x+2}=\dfrac {12}{35}\\ \\ \sf \implies \dfrac {x+2+x}{x (x+2)}=\dfrac {12}{35} \\ \\ \sf \implies \dfrac {2x+2}{x^2+2x}=\dfrac {12}{35} \\ \\ \sf \implies 35(2x+2)=12 (x^2+2x)=0 \\ \\ \sf \implies 70x+70=12x^2+24x=0 \\ \\ \sf \implies -12x^2+70x-24x+70=0 \\ \\ \sf \implies -(12x^2-46x-70)=0 \\ \\ \sf \implies 2 (6x^2-23x-35)=0 \\ \\ \sf \implies 6x^2-30x+7x-35=0 \\ \\ \sf \implies 6x (x-5)+7 (x-5)=0 \\ \\ \sf \implies (x-5)(6x+7)=0 \\ \\ \sf \implies x-5=0\: \: \:6x+7=0 \\ \\ \sf x=5\: or \:x=-7/6 \\ \\ \sf We\:will\:take\:x=5\:because\:-7/6\: \\ \\ \sf is\:not\:odd \\ \\ \sf Hence,First\:Number=x=5 \\ \\ \sf and\:Second \:number =x+2=5+2=7$

❤hope it helps you ❤

#Be Brainly

Answer 2

Answer:X=5&7

Step-by-step explanation:Let 1st odd natural number =X

Consecutive odd natural number =X+2

Reciprocal of both 1/X and 1/X+2

1/X+1/X+2=12/35

(X+2)+X/X(X+2)=12/35

X+2+X/X(X+2)=12/35

2X+2/X(X+2)=12/35

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

2(X+1)×35=12×X(X+2)

(X+1)×35=6X(X+2)

35X+35=6(X^2+2X)

35X+35=6X^2+12X

6X^2+12X-35X-35=0

6X^2+23X-35=0

6X^2+30X-7X-35=0

6X(X+5)-7(X+5)=0

(X+5)(6X-7)=0

X+5=0, 6X-7=0

X=5 , X=7/6

Therefore, X=5 and 7