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# simultaneous system

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$$\large{\\ \\ \begin{cases} { a }^{ 4 }+{ ( ab ) }^{ 2 }+{ b }^{ 4 }=900 \\ { a }^{ 2 }+ab+{ b }^{ 2 }=45 \end{cases}}$$

Let a and b be real numbers that satisfy the equation above. Find the value of 2ab.

Jul 28, 2020

$$\displaystyle a^{4}+(ab)^{2}+b^{4}=\{(a^{2}+b^{2})-ab\} \{(a^{2}+b^{2})+ab\}=900, \\ \text{substituting the second equation,}\\ (a^{2}+b^{2}-ab).45=900,\\ \text{so,}\\ a^{2}+b^{2}-ab=20,\\ \text{and now subtract this from the second equation.}$$