Diketahui p = √5 + √7 dan q = √7 - √5, maka p(pangkat)2 - q(pangkat)2 =
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![\displaystyle p=\sqrt5+\sqrt7\text{ dan }q=\sqrt7-\sqrt5\\\\\text{cara 1 : pemfaktoran}\\p^2-q^2=(p+q)(p-q)\\p^2-q^2=(\sqrt5+\sqrt7+\sqrt7-\sqrt5)(\sqrt5+\sqrt7-[\sqrt7-\sqrt5])\\p^2-q^2=(2\sqrt7)(\sqrt5+\sqrt7-\sqrt7+\sqrt5)\\p^2-q^2=(2\sqrt7)(2\sqrt5)\\\boxed{\boxed{p^2-q^2=4\sqrt{35}}}\\\\\text{cara 2 : mencari masing - masing nilai}\\p^2=(\sqrt5+\sqrt7)^2\\p^2=5+2\sqrt{35}+7\\p^2=12+2\sqrt{35}\\\\q^2=(\sqrt7-\sqrt5)^2\\q^2=7-2\sqrt{35}+5\\q^2=12-2\sqrt{35}\\\\\text{sehingga :}](https://tex.z-dn.net/?f=%5Cdisplaystyle+p%3D%5Csqrt5%2B%5Csqrt7%5Ctext%7B+dan+%7Dq%3D%5Csqrt7-%5Csqrt5%5C%5C%5C%5C%5Ctext%7Bcara+1+%3A+pemfaktoran%7D%5C%5Cp%5E2-q%5E2%3D%28p%2Bq%29%28p-q%29%5C%5Cp%5E2-q%5E2%3D%28%5Csqrt5%2B%5Csqrt7%2B%5Csqrt7-%5Csqrt5%29%28%5Csqrt5%2B%5Csqrt7-%5B%5Csqrt7-%5Csqrt5%5D%29%5C%5Cp%5E2-q%5E2%3D%282%5Csqrt7%29%28%5Csqrt5%2B%5Csqrt7-%5Csqrt7%2B%5Csqrt5%29%5C%5Cp%5E2-q%5E2%3D%282%5Csqrt7%29%282%5Csqrt5%29%5C%5C%5Cboxed%7B%5Cboxed%7Bp%5E2-q%5E2%3D4%5Csqrt%7B35%7D%7D%7D%5C%5C%5C%5C%5Ctext%7Bcara+2+%3A+mencari+masing+-+masing+nilai%7D%5C%5Cp%5E2%3D%28%5Csqrt5%2B%5Csqrt7%29%5E2%5C%5Cp%5E2%3D5%2B2%5Csqrt%7B35%7D%2B7%5C%5Cp%5E2%3D12%2B2%5Csqrt%7B35%7D%5C%5C%5C%5Cq%5E2%3D%28%5Csqrt7-%5Csqrt5%29%5E2%5C%5Cq%5E2%3D7-2%5Csqrt%7B35%7D%2B5%5C%5Cq%5E2%3D12-2%5Csqrt%7B35%7D%5C%5C%5C%5C%5Ctext%7Bsehingga+%3A%7D "\displaystyle p=\sqrt5+\sqrt7\text{ dan }q=\sqrt7-\sqrt5\\\\\text{cara 1 : pemfaktoran}\\p^2-q^2=(p+q)(p-q)\\p^2-q^2=(\sqrt5+\sqrt7+\sqrt7-\sqrt5)(\sqrt5+\sqrt7-[\sqrt7-\sqrt5])\\p^2-q^2=(2\sqrt7)(\sqrt5+\sqrt7-\sqrt7+\sqrt5)\\p^2-q^2=(2\sqrt7)(2\sqrt5)\\\boxed{\boxed{p^2-q^2=4\sqrt{35}}}\\\\\text{cara 2 : mencari masing - masing nilai}\\p^2=(\sqrt5+\sqrt7)^2\\p^2=5+2\sqrt{35}+7\\p^2=12+2\sqrt{35}\\\\q^2=(\sqrt7-\sqrt5)^2\\q^2=7-2\sqrt{35}+5\\q^2=12-2\sqrt{35}\\\\\text{sehingga :}")
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