If 'x' satisfies equation [x+0.19] + [x+0.20] + -----+ [x +0.91] =542 then [100x] is (where [.] repersents greatest integer function)

Open in App

Solution

Total 73 terms. So 542 $= 73 \times 7 + 31$
So some terms have [.] value as 7 & some have 8.
So least 31 terms should have value 8.
So $[] + - - - - +      7 \times 42 [x + 61] + - - - - + [0 + 91]      8 \times 91$
$x + 0.61 = 8$
$x = 7.39$
So x will be 7.39.....
So 100x =739.....
So [100x] =739

Suggest Corrections

Similar questions

[\frac{x}{49}] = [\frac{x}{51}]

[.]

x \in [0, 10]

x

x^{2} + 4 x + [x] + 6 = 0

The value of $lim x \to 0 ([\frac{100 x}{s i n x}] + [\frac{99 s i n x}{x}])$ ,where [.] denotes the greatest integer function, is

[cos x] + [sin x + 1] = 0

x

f (x)

x \in [0, 2 π]

[]

Join BYJU'S Learning Program