the house of a row are numbered consecutively from 1 to 49. show that there is a value of x such that the sum of the numbers of the house proceeding the house number x is equal to the sum of the numbers of the house following .it find the value of x.
Give proper explanation...
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Answer:
35
Step-by-step explanation:
1+2+3+...+(x-1)=(x+1)+(x+2)+....+49
1+2+3+....+(x-1)=1+2+3.....+x+(x-1).....+49 - [1+2+3+...+x]
[x-1]/2*[1+x-1]=49/2*[49-1]-x/2[1+x]
=x(x-1)=49*50-x(x+1)
=x² - x + x² +x = 49*50
=2 *x²=49*50
x²=47 *50
x= √ (47*25)
x=7*5=35
utsavmjoshi:
mark it brainliest
explain the second step pls
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