x=-1+√1+4(2)(52)/4=-1+√4225/4=-1+65/4

i.e.,x=64/4 or nox=-33/2

x=16 or x=-33/2

Since x cannot be negativeSo, the breadth of the plot is 16 metres of the plot is (2x + 1) = 33m

You should verify that these values satisfy the conditions of the problem.





Example-9.. Find two consecutive positive odd integers, sum of whose squares is 290.

Solution: Let the first positive odd integer be xThen, the second integer will bex+2. According to the question,

x ^ 2 + (x + 2) ^ 2 = 290

ie.. x²+x²+4x+4=290

i.c.. 2x ^ 2 + 4x - 286 = 0

i.e., x²+2x-143=0

which is a quadratic equation in x

Using the quadratic formula x = (- b plus/minus sqrt(b ^ 2 - 4ac))/2

we get ,x= -2 pm sqrt 4+572 2 = -2 pm sqrt 576 2 = -2 pm24 2

i e * x = 1 or x=-13

But x is given to be positive odd integerTherefore, x-13. Thus, the two consecutive odd integers are 11 and 1(x + 2) = 11 + 2 = 13 .

Check: 11 ^ 2 + 13 ^ 2 = 121 + 169 = 290 .

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