Please solve question number 5...... I will mark you as the brainliest.......... Please please please please solve this fast.....
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Let the numerator be a
Denominator = 2a + 1
Fraction = a / (2a + 1)
According to question,
a / (2a + 1) + (2a+1) / a = 2 16 /21
=> [ a^2 + (2a+1)^2] / a(2a +1) = 58 /21
=> ( a^2 + 4a^2 + 4a + 1) / (2a^2 + a) = 58 /21
=> ( 5a^2 + 4a + 1) / (2a^2 + a) = 58 /21
=> 105a^2 + 84a + 21 = 116a^2 + 58a
=> 11a^2 - 26a - 21 = 0
=> 11a^2 - 33a + 7a - 21 = 0
=> 11a ( a - 3) + 7 ( a - 3) = 0
=> (a-3) (11a + 7) = 0
a = 3 and - 7 /11
Neglecting negative value, we get
a = 3
Required fraction = 3 / (2 × 3 + 1)
= 3 / 7
Denominator = 2a + 1
Fraction = a / (2a + 1)
According to question,
a / (2a + 1) + (2a+1) / a = 2 16 /21
=> [ a^2 + (2a+1)^2] / a(2a +1) = 58 /21
=> ( a^2 + 4a^2 + 4a + 1) / (2a^2 + a) = 58 /21
=> ( 5a^2 + 4a + 1) / (2a^2 + a) = 58 /21
=> 105a^2 + 84a + 21 = 116a^2 + 58a
=> 11a^2 - 26a - 21 = 0
=> 11a^2 - 33a + 7a - 21 = 0
=> 11a ( a - 3) + 7 ( a - 3) = 0
=> (a-3) (11a + 7) = 0
a = 3 and - 7 /11
Neglecting negative value, we get
a = 3
Required fraction = 3 / (2 × 3 + 1)
= 3 / 7
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