Math, asked by kashanrangrezz, 1 year ago

the sum of three consecutive numbers in an A.P is 21 and their product is 231.find the numbers.class X

Answers

Answered by swastikswarup4
0
so
this is the
a p
that is 3 7 11
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swastikswarup4: can u give me brsimliedt ans
Answered by shadowsabers03
0

\bold{Answer:}

\bold{3, 7, 11}

\bold{Step}$-$\bold{by}$-$\bold{step\ explanation:}

$$Let the three numbers be$\ \ x - d,\ x,\ x + d \\ \\ $Sum$ \\ \\ \frac{3}{2}[x - d + x + d] = 21 \\ \\ \frac{3}{2} \times 2x = 21 \\ \\ 3x = 21 \\ \\ x = 21 \div 3 = \bold{7} \\ \\ \\


$$So we found the middle term among the three. \\ \\ Now let's find the common difference. \\ \\


$$Product$ \\ \\ x(x - d)(x + d) = 231 \\ \\ 7(7 - d)(7 + d) = 231 \\ \\ (7 - d)(7 + d) = 231 \div 7 \\ \\ 7^2 - d^2 = 33 \ \ \ \ \ \ \ \ \ \ \ \ [(a - b)(a + b) = a^2 - b^2] \\ \\ 49 - d^2 = 33 \\ \\ d^2 = 49 - 33 \\ \\ d^2 = 16 \\ \\ d = \sqrt{16} \\ \\ d = \pm 4 \\ \\ d = 4 \ \ \ \ \ $OR$\ \ \ \ \ d = -4 \\ \\ \\


$$If$\ \ d = 4, \\ \\ x - d = 7 - 4 = \bold{3} \\ \\ x + d = 7 + 4 = \bold{11} \\ \\ \\ $If$\ \ d = -4, \\ \\ x - d = 7 - (-4) = 7 + 4 = \bold{11} \\ \\ x + d = 7 + (-4) = 7 - 4 = \bold{3} \\ \\ \\ \therefore\ $The terms are$\ \ \bold{3, 7}\ $and$\ \bold{11}.


$$Hope this may be helpful. \\ \\ Please mark my answer as the$\ \bold{brainliest}\ $if this may be helpful. \\ \\ Thank you. Have a nice day.$ \\ \\ \\ \#adithyasajeevan

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