IIT JEE , AIEEE Forum - Mathematics , Algebra

m.viddya

Q.(15+4^{[ ]}

14)^x2-7x+11+(15-4^{[ ]}

14)^x2-7x+11=30.then the no.of real values of x are?

m.viddya

Please note:in the above question it is x to the power of 2 and not 2x...

chimanshu_007

Hey in these type of qs....

a^f(x) + b^f(x) = a + b

and ab = 1.....it always give f(x) = 1 and f(x) = -1

so

x² -7x+11 = 1 , x² -7x + 11 = -1

now solve

chimanshu_007

the other method

(15 + 4 root14)(15-4root14) = 225 - 224 = 1

(15 + 4root14) = 1 / (15 - 4root14)

soo

(15 + 4root14)^{x^2 -7x+11} + 1/ (15 + 4root14)^{x^2-7x+11} = 30

(15 + 4root14)^{x^2-7x +11} = y

y + 1/y = 30

y comes out to be

15+_4root14

now take 1ce 15 + 4root14 = (15 + 4root14)^{x^2-7x+11}

then....try

the other 1...

cheers!

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