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Maths-

General

Easy

Question

$0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3$ and the equation $x squared plus 4 plus 3 cos space left parenthesis a x plus b right parenthesis equals 2 x$ has at least one solution then the value of (a+b)

$\frac{π}{2}$
$\frac{π}{4}$
$\frac{π}{3}$
$π$

hint Hint:

In this question, we have to find the value of (a +b) if $0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3$ and the equation $x squared plus 4 plus 3 cos space left parenthesis a x plus b right parenthesis equals 2 x$ has at least one solution. For that first we will solve the given equation to find all the possible value and later examine it with the condition given to find the required answer.

The correct answer is: $pi$

$x squared plus 4 plus 3 space cos space left parenthesis a x plus c right parenthesis equals 2 x rightwards double arrow x squared minus 2 x plus 4 plus 3 space cos space left parenthesis a x plus b right parenthesis equals 0 rightwards double arrow left parenthesis x minus 1 right parenthesis squared plus 3 equals negative 3 c o s left parenthesis a x plus b right parenthesis L e t space f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis squared plus 3 space a n d space f left parenthesis x right parenthesis equals negative 3 space cos space left parenthesis a x plus b right parenthesis I f space x equals 1 comma space L H S space equals 3 space a n d space R H S equals negative 3 cos left parenthesis a plus b right parenthesis S o comma space minus 3 cos left parenthesis a plus b right parenthesis equals 3 rightwards double arrow cos left parenthesis a plus b right parenthesis equals negative 1 rightwards double arrow a plus b space equals pi comma space 3 pi comma space 5 pi B u t space 0 less or equal than a less or equal than 3 comma 0 less or equal than b less or equal than 3 rightwards double arrow a plus b equals pi$

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