Track / Stage 4 / 86 of 340 #346 of 1964

If $(y-5)^{2}=(y-9)^{2}$, what is the value of $y$ ?

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A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Expanding both sides, we have $y^{2}-10 y+25=y^{2}-18 y+81$.

Rearranging, we have $8 y=56$, so $y=7$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.