Jack is thinking of two positive numbers, one of them is 4 more than the other and the sum of their squares is 208 what are the numbers?
x = one number
x + 4 = other number {one of them is 4 more than the other}
x² + (x + 4)² = 208 {the sum of their squares is 208}
x² + (x + 4)(x + 4) = 208 {when squaring a binomial, multiply it by itself}
x² + x² + 8x + 16 = 208 {used foil method}
2x² + 8x + 16 = 208 {combined like terms}
2x² + 8x - 192 = 0 {subtracted 208 from both sides}
2(x² + 4x - 96) = 0 {factored 2 out}
2(x + 12)(x - 8) = 0 {factored into two binomials}
x + 12 = 0 or x - 8 = 0 {set each factor equal to 0}
x = -12 or x = 8 {solved each equation for x}
x = 8 {taking only positive integers}
x + 4 = 12 {substituted 8, in for x, into x + 4}
8 and 12 are the numbers
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