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`(a-d)^(2)``(ad)^(2)``(a+d)^(2)``(a//d)^(2)`

Answer :

ASolution :

Let r be the common ratio of the G.P., a,b,c,d. Then, <br> `b=ar,c=ar^(2) and d=ar^(3)` ltbrRgt `therefore(b-c)^(2)+(c-a)^(2)+(d-b)^(2)` <br> `=(ar-ar^(2))^(2)+(ar^(2)-a)^(2)+(ar^(3)-ar)^(2)` <br> `=a^(r )r^(2)(1-r)^(2)+a^(2)(r^(2)-1)^(2)+a^(2)r^(2)(r^(2)-1)^(2)` <br> `=a^(2)(r^(6)-2r^(3)+1)` <br> `=a^(2)(1-r^(3))^(2)` <br> `=(a-ar^(3))^(2)` <br> `=(a-d)^(2)`Transcript

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00:00 - 00:59 | Soheb question is if a b c d are in GP then B minus C whole square + c minus A square + b minus b whole square equal to write so we can write a equal to a b is equal to a are equal to wear a square and Aadi equal to a r cube right now we have a b minus C whole square + c minus a whole square + b minus C whole square right so we will solve this we will put the value of be here be a b c d hair side so this comes a r minus A square whole square + b square minus A square |

01:00 - 01:59 | B equal to a r minus Q whole square right this will come I will take my a common right so this will come as a square are square 1 - are whole square + a square are square minus 1 whole square + a square square square minus 1 whole square write this will come out as a this will come out as a square are to the power |

02:00 - 02:59 | -2 R Cube + 1 write this week and write it as a week and write it as the a square 1 - r-cube whole square that is 1 - 6 cube square will be one plus 8 to the power 6 - 2 are you right here right now we will take this is inside this this will become a minus b cube this is here are you here side so this is a h q whole square 9 this a cube is equal to de |

03:00 - 03:59 | comes as a minus b whole square |

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