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Question

After solving the equation (5x+2)2+(5x2)2(5x+2)2(5x2)2=1312, solution set for x is {m,0.27}. Then, the value of m is:

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Solution

Given (5x+2)2+(5x2)2(5x+2)2(5x2)2=1312
Applying the formulae, (a+b)2+(ab)2=2(a2+b2)
and (a+b)2(ab)2=4ab where a=5x;b=2
2((5x)2+22)4×(5x)×2=1312
25x2+420x=1312
On cross multiplying and simplifying,
75x265x+12=0
75x220x45x+12=0
5x(15x4)3(15x4)=0
(5x3)(15x4)=
x={35,415}={0.6,0.27}
Hence, m=0.6

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