Answer-If a + b + c = 19, a2 + b2 + c2 = 133 and ac = y2 , then the difference between c and a is:

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Given, x  y  z  19,  a2  b2  c2  133 and ab  y2   We know, a  b  c2  a2  b2  c2   2  ab  bc  ac  Or, 192  133  2  ab  bc  ac  Or, ab  bc  ca  361  133  2  Or, ab  bc  ca  114  Or, ab  bc  b2   114  Or, ba  b  c  114  Or, b  19  114  Or, b  11419  6  Therefore, ac  62  36  Therefore, possible values of a and c  are 4 or 9  Required difference  9  4  5

If a + b + c = 19, a2 + b2 + c2 = 133 and ac = y2 , then the difference between c and a is:

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