Use the information provided to answer Part A and Part B.
Consider the equation (x² + 3)² + 21 = 10x² + 30.
Part A
If u = x² + 3, then replace the x² + 3 with u (x² + 3)² + 21 = 10(x² + 3) {factored 10 out of right side} u² + 21 = 10u {replaced (x² + 3) with u} u²  10u + 21 = 0 {subtracted 10u from each side} D.) u²  10u + 21 = 0
Part B
Solve the equation u²  10u + 21 = 0 for u u²  10u + 21 = 0 (u  7)(u  3) = 0 {factored into two binomials} u  7 = 0 or u  3 = 0 {set each factor equal to 0} u = 7 or u = 3 {solved each equation for u} If u = x² + 3, then x² + 3 = 7 or x² + 3 = 3 {substituted x² + 3 in for u} x² = 4 or x² = 0 {subtracted 3 from each side of each equation} x = 2 or 2 or 0 {took the square root of each side of each equation} C.) 2 D.) 0 E.) 2 Ask Algebra House Comments are closed.

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